Rigid body dynamics of mechanisms
Hahn, Hubert
2003-01-01
The second volume of Rigid Body Dynamics of Mechanisms covers applications via a systematic method for deriving model equations of planar and spatial mechanisms. The necessary theoretical foundations have been laid in the first volume that introduces the theoretical mechanical aspects of mechatronic systems. Here the focus is on the application of the modeling methodology to various examples of rigid-body mechanisms, simple planar ones as well as more challenging spatial problems. A rich variety of joint models, active constraints, plus active and passive force elements is treated. The book is intended for self-study by working engineers and students concerned with the control of mechanical systems, i.e. robotics, mechatronics, vehicles, and machine tools. The examples included are a likely source from which to choose models for university lectures.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Compared with the traditional rigid-plastic/rigid-viscoplastic(RP/RVP) FEM(based on iteration solution),RP/RVP FEM based on linear programming (LP) has some remarkable advantages,such as it's free of convergence problem and its convenience in contact,rigid zone,and friction force treatment.The numerical model of RP/RVP FEM based on LP for axisymmetrical metal forming simulation is studied,and some related key factors and its treatment methods in formulation of constraint condition are proposed.Some solution examples are provided to validate its accuracy and efficiency.
Rigid multibody system dynamics with uncertain rigid bodies
Energy Technology Data Exchange (ETDEWEB)
Batou, A., E-mail: anas.batou@univ-paris-est.fr; Soize, C., E-mail: christian.soize@univ-paris-est.fr [Universite Paris-Est, Laboratoire Modelisation et Simulation Multi Echelle, MSME UMR 8208 CNRS (France)
2012-03-15
This paper is devoted to the construction of a probabilistic model of uncertain rigid bodies for multibody system dynamics. We first construct a stochastic model of an uncertain rigid body by replacing the mass, the center of mass, and the tensor of inertia by random variables. The prior probability distributions of the stochastic model are constructed using the maximum entropy principle under the constraints defined by the available information. The generators of independent realizations corresponding to the prior probability distribution of these random quantities are further developed. Then several uncertain rigid bodies can be linked to each other in order to calculate the random response of a multibody dynamical system. An application is proposed to illustrate the theoretical development.
Measuring the Acceleration of a Rigid Body
Directory of Open Access Journals (Sweden)
Peter G. Martin
1998-01-01
Full Text Available Two methods to measure the six-degree-of-freedom acceleration of a point on a rigid body are presented. The first, referred to as the periphery scheme, makes use of three clusters of accelerometers mounted orthogonal to each other and coincident with the axes of the point. One of the clusters consists of the three accelerometers attached to a cube-shaped triaxial angular rate sensor (ARS. The second method, called the compact cube scheme, uses a single 3-accelerometer/ARS cluster that may be mounted anywhere on the rigid body. During impact tests with an instrumented rigid body, both methods produced measurements that were highly correlated near the time of peak acceleration. Whereas the compact cube scheme was more economical and easier to implement, the periphery scheme produced results that were less disrupted by instrument signal errors and noisy environments.
Stability of flow over axisymmetric bodies with porous suction strips
Nayfeh, A. H.; Reed, H. L.
1982-01-01
Linear triple deck, closed form solutions for mean-flow quantities are developed for axisymmetric incompressible flow past a body with porous strips. The solutions account for upstream influence and are linear superpositions of the flow past the body without suction plus the perturbations due to the suction strips. Flow past the suctionless body is calculated using the Transition Analysis Program System, and a simple linear optimization scheme to determine number, spacing, and mass flow rate through the strips on an axisymmetric body is developed using the linear, triple-deck, closed-form solutions. The theory is demonstrated by predicting optimal strip distributions, and the effect of various adverse pressure-gradient situations on stability is studied.
Rings of non-spherical, axisymmetric bodies
Gupta, Akash; Sharma, Ishan
2016-01-01
We investigate the dynamical behavior of rings around bodies whose shapes depart considerably from that of a sphere. To this end, we have developed a new self-gravitating discrete element N-body code, and employed a local simulation method to simulate a patch of the ring. The central body is modeled as a symmetric (oblate or prolate) ellipsoid, or defined through the characteristic frequencies (circular, vertical, epicyclic) that represent its gravitational field. Through our simulations we explore how a ring's behavior -- characterized by dynamical properties like impact frequency, granular temperature, number density, vertical thickness and radial width -- varies with the changing gravitational potential of the central body. We also contrast properties of rings about large central bodies (e.g. Saturn) with those of smaller ones (e.g. Chariklo). Finally, we investigate how the characteristic frequencies of a central body, restricted to being a solid of revolution with an equatorial plane of symmetry, affect ...
On the stability of compressible flow past axisymmetric bodies
Malik, M. R.; Spall, R. E.
1991-01-01
Compressible linear stability theory for axisymmetric flows is presented. The theory is applied to flow past a cylinder and a sharp cone at a Mach number of 5 with adiabatic wall conditions. The effect of transverse curvature and body divergence is studied. It is found that transverse curvature has a stabilizing influence on axisymmetric (first and second mode) disturbances while it has a destabilizing influence on the asymmetric (oblique first mode) disturbances. The body divergence effects are stabilizing for both symmetric and asymmetric disturbances. Comparisons made with the results of planar stability theory show that, for a cylinder, curvature effects become more pronounced with increasing distance along the cylinder. For a sharp cone, these effects become less significant further away from the cone tip since the body radius increases faster than the growth of the boundary layer. The effect of cone angle on stability is also studied.
Rigid body dynamics on the Poisson torus
Richter, Peter H.
2008-11-01
The theory of rigid body motion with emphasis on the modifications introduced by a Cardan suspension is outlined. The configuration space is no longer SO(3) but a 3-torus; the equivalent of the Poisson sphere, after separation of an angular variable, is a Poisson torus. Iso-energy surfaces and their bifurcations are discussed. A universal Poincaré section method is proposed.
Geometric integrators for stochastic rigid body dynamics
Tretyakov, Mikhail
2016-01-05
Geometric integrators play an important role in simulating dynamical systems on long time intervals with high accuracy. We will illustrate geometric integration ideas within the stochastic context, mostly on examples of stochastic thermostats for rigid body dynamics. The talk will be mainly based on joint recent work with Rusland Davidchak and Tom Ouldridge.
PRESSURE AND PRESSURE GRADIENT IN AN AXISYMMETRIC RIGID VESSEL WITH STENOSIS
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Based on an improvement of the Karman-Pohlhausen's method, using nonlinear polynomial fitting and numerical integral, the axial distributions of pressure and its gradient in an axisymmetric rigid vessel with stenosis were obtained, and the distributions related to Reynolds number and the geometry of stenotic vessel were discussed. It shows that with the increasing of stenotic degree or Reynolds number, the fluctuation of pressure and its gradient in stenotic area is intense rapidly, and negative pressure occurs subsequently in the diverging part of stenotic area. Especially when the axial range of stenosis extends, the flow of blood in the diverging part will be more obviously changed.In higher Reynolds number or heavy stenosis, theoretical calculation is mainly in accordance with past experiments.
The two-body problem of a pseudo-rigid body and a rigid sphere
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall; Vereshchagin, M.; Gózdziewski, K.;
2012-01-01
n this paper we consider the two-body problem of a spherical pseudo-rigid body and a rigid sphere. Due to the rotational and "re-labelling" symmetries, the system is shown to possess conservation of angular momentum and circulation. We follow a reduction procedure similar to that undertaken...... in the study of the two-body problem of a rigid body and a sphere so that the computed reduced non-canonical Hamiltonian takes a similar form. We then consider relative equilibria and show that the notions of locally central and planar equilibria coincide. Finally, we show that Riemann's theorem on pseudo......-rigid bodies has an extension to this system for planar relative equilibria....
Numerical simulation of cavitating flow past axisymmetric body
Directory of Open Access Journals (Sweden)
Dong-Hyun Kim
2012-09-01
Full Text Available Cavitating flow simulation is of practical importance for many engineering systems, such as marine propellers, pump impellers, nozzles, torpedoes, etc. The present work has developed the base code to solve the cavitating flows past the axisymmetric bodies with several forebody shapes. The governing equation is the Navier-Stokes equation based on homogeneous mixture model. The momentum is in the mixture phase while the continuity equation is solved in liquid and vapor phase, separately. The solver employs an implicit preconditioning algorithm in curvilinear coordinates. The computations have been carried out for the cylinders with hemispherical, 1-caliber, and 0-caliber forebody and, then, compared with experiments and other numerical results. Fairly good agreements with experiments and numerical results have been achieved. It has been concluded that the present numerical code has successfully accounted for the cavitating flows past axisymmetric bodies. The present code has also shown the capability to simulate ventilated cavitation.
Adaptive Control of Rigid Body Satellite
Institute of Scientific and Technical Information of China (English)
Thawar T. Arif
2008-01-01
The minimal controller synthesis (MCS) is an extension of the hyperstable model reference adaptive control algorithm. The aim of minimal controller synthesis is to achieve excellent closed-loop control despite the presence of plant parameter variations, external disturbances, dynamic coupling within the plant and plant nonlinearities. The minimal controller synthesis algorithm was successfully applied to the problem of decentralized adaptive schemes. The decentralized minimal controller synthesis adaptive control strategy for controlling the attitude of a rigid body satellite is adopted in this paper. A model reference adaptive control strategy which uses one single three-axis slew is proposed for the purpose of controlling the attitude of a rigid body satellite. The simulation results are excellent and show that the controlled system is robust against disturbances.
Quantum mechanics of a generalised rigid body
Gripaios, Ben
2015-01-01
We consider the quantum version of Arnold's generalisation of a rigid body in classical mechanics. Thus, we quantise the motion on an arbitrary Lie group manifold of a particle whose classical trajectories correspond to the geodesics of any one-sided-invariant metric. We show how the derivation of the spectrum of energy eigenstates can be simplified by making use of automorphisms of the Lie algebra and (for groups of Type I) by methods of harmonic analysis. As examples, we consider all connected and simply-connected Lie groups up to dimension 3. This includes the universal cover of the archetypical rigid body, along with a number of new exactly-solvable models. We also discuss a possible application to the topical problem of quantising a perfect fluid.
Pulling rigid bodies through granular material
Kubik, Ryan; Dressaire, Emilie
2016-11-01
The need for anchoring systems in granular materials such as sand is present in the marine transportation industry, e.g. to layout moorings, keep vessels and docks fixed in bodies of water, build oil rigs, etc. The holding power of an anchor is associated with the force exerted by the granular media. Empirical evidence indicates that the holding power depends on the size and shape of the anchoring structure. In this model study, we use a two-dimensional geometry in which a rigid body is pulled through a granular media at constant velocity to determine the drag and lift forces exerted by a granular medium on a moving object. The method allows measuring the drag force and recording the trajectory of the rigid object through the sand. We systematically vary the size and geometry of the rigid body, the properties of the granular medium and the extraction speed. For different initial positions of a cylindrical object pulled horizontally through the medium, we record large variations in magnitude of the drag and a significant lift force that pulls the object out of the sand.
Axisymmetric scattering of an acoustical Bessel beam by a rigid fixed spheroid.
Mitri, Farid G
2015-10-01
Based on the partial-wave series expansion (PWSE) method in spherical coordinates, a formal analytical solution for the acoustic scattering of a zeroth-order Bessel acoustic beam centered on a rigid fixed (oblate or prolate) spheroid is provided. The unknown scattering coefficients of the spheroid are determined by solving a system of linear equations derived for the Neumann boundary condition. Numerical results for the modulus of the backscattered pressure (θ = π) in the near field and the backscattering form function in the far field for both prolate and oblate spheroids are presented and discussed, with particular emphasis on the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid), the half-cone angle of the Bessel beam, and the dimensionless frequency. The plots display periodic oscillations (versus the dimensionless frequency) because of the interference of specularly reflected waves in the backscattering direction with circumferential Franz' waves circumnavigating the surface of the spheroid in the surrounding fluid. Moreover, the 3-D directivity patterns illustrate the near- and far-field axisymmetric scattering. Investigations in underwater acoustics, particle levitation, scattering, and the detection of submerged elongated objects and other related applications utilizing Bessel waves would benefit from the results of the present study.
Rigid Body Mechanics Mathematics, Physics and Applications
Heard, William B
2005-01-01
This textbook is a modern, concise and focused treatment of the mathematical techniques, physical theories and applications of rigid body mechanics, bridging the gap between the geometric and more classical approaches to the topic. It emphasizes the fundamentals of the subject, stresses the importance of notation, integrates the modern geometric view of mechanics and offers a wide variety of examples -- ranging from molecular dynamics to mechanics of robots and planetary rotational dynamics. The author has unified his presentation such that applied mathematicians, mechanical and astro-aerodyna
Brownian dynamics of confined rigid bodies
Energy Technology Data Exchange (ETDEWEB)
Delong, Steven; Balboa Usabiaga, Florencio; Donev, Aleksandar, E-mail: donev@courant.nyu.edu [Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 (United States)
2015-10-14
We introduce numerical methods for simulating the diffusive motion of rigid bodies of arbitrary shape immersed in a viscous fluid. We parameterize the orientation of the bodies using normalized quaternions, which are numerically robust, space efficient, and easy to accumulate. We construct a system of overdamped Langevin equations in the quaternion representation that accounts for hydrodynamic effects, preserves the unit-norm constraint on the quaternion, and is time reversible with respect to the Gibbs-Boltzmann distribution at equilibrium. We introduce two schemes for temporal integration of the overdamped Langevin equations of motion, one based on the Fixman midpoint method and the other based on a random finite difference approach, both of which ensure that the correct stochastic drift term is captured in a computationally efficient way. We study several examples of rigid colloidal particles diffusing near a no-slip boundary and demonstrate the importance of the choice of tracking point on the measured translational mean square displacement (MSD). We examine the average short-time as well as the long-time quasi-two-dimensional diffusion coefficient of a rigid particle sedimented near a bottom wall due to gravity. For several particle shapes, we find a choice of tracking point that makes the MSD essentially linear with time, allowing us to estimate the long-time diffusion coefficient efficiently using a Monte Carlo method. However, in general, such a special choice of tracking point does not exist, and numerical techniques for simulating long trajectories, such as the ones we introduce here, are necessary to study diffusion on long time scales.
Understanding rigid body motion in arbitrary dimensions
Leyvraz, Francois
2014-01-01
Why would anyone wish to generalize the already unappetizing subject of rigid body motion to an arbitrary number of dimensions? At first sight, the subject seems to be both repellent and superfluous. The author will try to argue that an approach involving no specifically three-dimensional constructs is actually easier to grasp than the traditional one and might thus be generally useful to understand rigid body motion both in three dimensions and in the general case. Specific differences between the viewpoint suggested here and the usual one include the following: here angular velocities are systematically treated as antisymmetric matrices, a symmetric tensor $I$ quite different from the moment of inertia tensor plays a central role, whereas the latter is shown to be a far more complex object, namely a tensor of rank four. A straightforward way to define it is given. The Euler equation is derived and the use of Noether's theorem to obtain conserved quantities is illustrated. Finally the equation of motion for ...
The theory of pseudo-rigid bodies
Cohen, Harley
1988-01-01
This monograph concerns the development, analysis, and application of the theory of pseudo-rigid bodies. It collects together our work on that subject over the last five years. While some results have appeared else where, much of the work is new. Our objective in writing this mono graph has been to present a new theory of the deformation of bodies, one that has not only a firm theoretical basis, but also the simplicity to serve as an effective tool in practical problems. Consequently, the main body of the treatise is a multifaceted development of the theory, from foundations to explicit solutions to linearizations to methods of approximation. The fact that this variety of aspects, each examined in considerable detail, can be collected together in a single, unified treat ment gives this theory an elegance that we feel sets it apart from many others. While our goal has always been to give a complete treatment of the theory as it now stands, the work here is not meant to be definitive. Theories are not ent...
Dual Quaternion Variational Integrator for Rigid Body Dynamic Simulation
XU, JIAFENG; Halse, Karl Henning
2016-01-01
We introduce a symplectic dual quaternion variational integrator(DQVI) for simulating single rigid body motion in all six degrees of freedom. Dual quaternion is used to represent rigid body kinematics and one-step Lie group variational integrator is used to conserve the geometric structure, energy and momentum of the system during the simulation. The combination of these two becomes the first Lie group variational integrator for rigid body simulation without decoupling translations and rotati...
Rigid Body Motion in Stereo 3D Simulation
Zabunov, Svetoslav
2010-01-01
This paper addresses the difficulties experienced by first-grade students studying rigid body motion at Sofia University. Most quantities describing the rigid body are in relations that the students find hard to visualize and understand. They also lose the notion of cause-result relations between vector quantities, such as the relation between…
Stability of rigid body rotation from a bond graph perspective
Breedveld, Peter
2009-01-01
This paper describes the history of the bond graph description of rigid body rotation dynamics and resolves a paradox that resulted from the common Euler Junction Structure (EJS) description of the exterior product in the Newton–Euler equation describing rigid body rotation [D.C. Karnopp, R.C. Rosen
Tautochrone and Brachistochrone Shape Solutions for Rocking Rigid Bodies
Glaschke, Patrick
2016-01-01
Rocking rigid bodies appear in several shapes in everyday life: As furniture like rocking chairs and rocking cradles or as toys like rocking horses or tilting dolls. The familiar rocking motion of these objects, a non-linear combination of a rigid rotation and a translation of the center of mass, gives rise to a number of interesting dynamical properties. However, their study has received little attention in the literature. This work presents a comprehensive introduction to the dynamics of rocking rigid bodies, including a concise derivation of the equations of motion as well as a general inversion procedure to construct rocking rigid body shapes with specified dynamical properties. Moreover, two novel rigid body shapes are derived - the tautochrone shape and the brachistochrone shape - which represent an intriguing generalization of the well-know tautochrone and brachistochrone curves. In particular, tautochrone shapes offer an alternative construction of a tautochrone pendulum, in addition to Huygens' cyclo...
Thin structured rigid body for acoustic absorption
Starkey, T. A.; Smith, J. D.; Hibbins, A. P.; Sambles, J. R.; Rance, H. J.
2017-01-01
We present a thin acoustic metamaterial absorber, comprised of only rigid metal and air, that gives rise to near unity absorption of airborne sound on resonance. This simple, easily fabricated, robust structure comprising a perforated metal plate separated from a rigid wall by a deeply subwavelength channel of air is an ideal candidate for a sound absorbing panel. The strong absorption in the system is attributed to the thermo-viscous losses arising from a sound wave guided between the plate and the wall, defining the subwavelength channel.
Stochastic modeling of uncertain mass characteristics in rigid body dynamics
Richter, Lanae A.; Mignolet, Marc P.
2017-03-01
This paper focuses on the formulation, assessment, and application of a modeling strategy of uncertainty on the mass characteristics of rigid bodies, i.e. mass, position of center of mass, and inertia tensor. These characteristics are regrouped into a 4×4 matrix the elements of which are represented as random variables with joint probability density function derived following the maximum entropy framework. This stochastic model is first shown to satisfy all properties expected of the mass and tensor of inertia of rigid bodies. Its usefulness and computational efficiency are next demonstrated on the behavior of a rigid body in pure rotation exhibiting significant uncertainty in mass distribution.
A Concise Introduction to Mechanics of Rigid Bodies Multidisciplinary Engineering
Huang, L
2012-01-01
A Concise Introduction to Mechanics of Rigid Bodies: Multidisciplinary Engineering presents concise, key concepts of kinematics and dynamics of rigid bodies. This compact volume bridges the steep gap between introductory texts on engineering mechanics, which focus on one and two dimensional motions of particles and rigid bodies, and advanced texts on multi-body dynamics in high dimension spaces found in multidisciplinary areas like mechatronics, robotics and biomechanics. In the book, rigid body motions in the spaces with different dimensions are described in addition to studies in a uniform framework supported by vector and matrix operations. Rigorous mathematic tools and explanations are provided to clarify the most complex concepts. This book also: Provides practical examples from different engineering areas, offering a link between theoretical fundamentals and everyday applications Offers simplified mathematical equations to clearly present essential theories in robotics and mechanics Presents statics...
Dynamical Equation of Post Newtonian Quasi-rigid Body
Institute of Scientific and Technical Information of China (English)
XU Chong-Ming; TAO Jin-He; HUANG Tian-Yi; WU Xue-Jun
2004-01-01
We derive the dynamical equation ofa post Newtonian (PN) quasi-rigid body from the general rotational equation of motion, I.e. The PN rotational equation of motion for a quasi-rigid body. It is emphasized that a rotational angular velocity vector and a figure axis besides the first post Newtonian (1PN) spin vector can be defined and realized for the model of a PN quasi-rigid body model constructed recently. Actually, we have shown that the moment of inertia tensor of a quasi-rigid body can be transformed into a diagonal form by an orthogonal transformation, which defines the principal axes of inertia of the body. As an example, its torque-free motion is discussed and a PN Poinsot configuration, which is similar to the Newtonian one with a small 1PN correction, is solved.
Institute of Scientific and Technical Information of China (English)
A.Avci; A.Bulu; A.Yapici
2006-01-01
A contact problem for an infinitely long hollow cylinder is considered.The cylinder is compressed by an outer rigid ring with a circular profile.The material of the cylinder is linearly elastic and isotropic.The extent of the contact region and the pressure distribution are sought.Governing equations of the elasticity theory for the axisymmetric problem in cylindrical coordinates are solved by Fourier transfoms and general expressions for the displacements are obtained.Using the boundary conditions,the formulation is reduced to a singular integral equation.This equation is solved by using the Gaussian quadrature.Then the pressure distribution on the contact region is determined.Numerical results for the contact pressure and the distance characterizing the contact area are given in graphical form.
Modeling the Collision with Friction of Rigid Bodies
Zabuga, A. G.
2016-09-01
Different models of a perfectly inelastic collision of rigid bodies in plane motion are compared. Formulas for the impact impulses are derived for the Kane-Levinson-Whittaker model based on the kinematic restitution factor, the Routh model based on the kinetic restitution factor, and the Stronge model based on the energy restitution factor. It is shown that these formulas coincide if the collision of rough rigid bodies in plane motion is perfectly inelastic
ADHESIVE CONTACT PROBLEM OF AXISYMMETRIC MINIATURE CIRCULAR PLATES WITH CENTRAL RIGID BUMP
Institute of Scientific and Technical Information of China (English)
Fu Yiming; Li Sheng; Tian Yanping
2006-01-01
Considering the adhesive effect and geometric nonlinearity, the adhesive contact between an elastic substrate and a clamped miniature circular plate with two different central rigid bumps under the action of uniform transverse pressure and in-plane tensile force in the radial direction was analyzed. And an analytical solution is presented by using the perturbation method. The relation of surface adhesive energies with critical load to detach the contacted surfaces is obtained. In the numerical results, the effects of adhesive energy, in-plane tensile force, rigid bump size and contact radius on the critical load are discussed, and the relation of critical contact radius with the gap between the central rigid bump and the substrate for different adhesive energies is investigated.
A fast impulsive contact suite for rigid body simulation.
Schmidl, Harald; Milenkovic, Victor J
2004-01-01
A suite of algorithms is presented for contact resolution in rigid body simulation under the Coulomb friction model: Given a set of rigid bodies with many contacts among them, resolve dynamic contacts (collisions) and static (persistent) contacts. The suite consists of four algorithms: 1) partial sequential collision resolution, 2) final resolution of collisions through the solution of a single convex QP (positive semidefinite quadratic program), 3) resolution of static contacts through the solution of a single convex QP, 4) freezing of "stationary" bodies. This suite can generate realistic-looking results for simple examples yet, for the first time, can also tractably resolve contacts for a simulation as large as 1,000 cubes in an "hourglass." Freezing speeds up this simulation by more than 25 times. Thanks to excellent commercial QP technology, the contact resolution suite is simple to implement and can be "plugged into" any simulation algorithm to provide fast and realistic-looking animations of rigid bodies.
A concise introduction to mechanics of rigid bodies multidisciplinary engineering
Huang, L
2017-01-01
This updated second edition broadens the explanation of rotational kinematics and dynamics — the most important aspect of rigid body motion in three-dimensional space and a topic of much greater complexity than linear motion. It expands treatment of vector and matrix, and includes quaternion operations to describe and analyze rigid body motion which are found in robot control, trajectory planning, 3D vision system calibration, and hand-eye coordination of robots in assembly work, etc. It features updated treatments of concepts in all chapters and case studies. The textbook retains its comprehensiveness in coverage and compactness in size, which make it easily accessible to the readers from multidisciplinary areas who want to grasp the key concepts of rigid body mechanics which are usually scattered in multiple volumes of traditional textbooks. Theoretical concepts are explained through examples taken from across engineering disciplines and links to applications and more advanced courses (e.g. industrial rob...
Hamiltonian dynamics of several rigid bodies interacting with point vortices
Weissmann, Steffen
2013-01-01
We introduce a Hamiltonian description for the dynamics of several rigid bodies interacting with point vortices in an inviscid, incompressible fluid. We adopt the idea of Vankerschaver et al. (2009) to derive the Hamiltonian formulation via symplectic reduction of a canonical Hamiltonian system on a principle fibre bundle. On the reduced phase space we determine the magnetic symplectic form directly, without resorting to the machinery of mechanical connections on principle fibre bundles. We derive the equations of motion for the general case, and also for the special Lie-Poisson case of a single rigid body and zero total vorticity. Finally we give a partly degenerate Lagrangian formulation for the system.
Kinematic Control of Free Rigid Bodies Using Dual Quaternions
Institute of Scientific and Technical Information of China (English)
Da-Peng Han; Qing Wei; Ze-Xiang Li
2008-01-01
This paper proposes a new type of control laws for free rigid bodies. The start point is the dual quaternion and its characteristics. The logarithm of a dual quaternion is defined, based on which kinematic control laws can be developed. Global exponential convergence is achieved using logarithmic feedback via a generalized proportional control law, and an appropriate Lyapunov function is constructed to prove the stability. Both the regulation and tracking problems are tackled. Omnidirectional control is discussed as a case study. As the control laws can handle the intercounection between the rotation and translation of a rigid body, they axe shown to be more applicable than the conventional method.
Axisymmetric scattering of an acoustical Bessel beam by a rigid fixed spheroid
Mitri, F G
2015-01-01
Based on the partial-wave series expansion (PWSE) method in spherical coordinates, a formal analytical solution for the acoustic scattering of a zeroth-order Bessel acoustic beam centered on a rigid fixed (oblate or prolate) spheroid is provided. The unknown scattering coefficients of the spheroid are determined by solving a system of linear equations derived for the Neumann boundary condition. Numerical results for the modulus of the backscattered pressure (\\theta = \\pi) in the near-field and the backscattering form function in the far-field for both prolate and oblate spheroids are presented and discussed, with particular emphasis on the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid), the half-cone angle of the Bessel beam \\beta, and the dimensionless frequency. The plots display periodic oscillations (versus the dimensionless frequency) due to the interference of specularly reflected waves in the backscattering direction with circumferential Franz' waves circumnavigati...
Completeness of General Solutions to Axisymmetric Problems of Transversely Isotropic Body
Institute of Scientific and Technical Information of China (English)
王炜; 徐新生; 王敏中
1994-01-01
In this paper a kind of problems,which are a little wider than the axisymmetric problems of a transversely isotropic elastic body,are considered in a rectangular coordinates system.Two new general solutions of the axisymmetric problems of a transversely isotropic body are concisely obtained in a cylindrical coordinates system.Their completeness is also proved.It is worth while pointing out thai whether the meridional half-section is simply connected or multiply connected,both the new general solutions are single-valued.Using these results eight special general solutions are derived,including some known famous solutions.
Euler-Poincare Reduction of Externall Forced Rigid Body Motion
DEFF Research Database (Denmark)
Wisniewski, Rafal; Kulczycki, P.
2004-01-01
. Assuming that the system possesses symmetry and the configuration manifold corresponds to a Lie group, the Euler-Poincaré reduction breaks up the motion into separate equations of dynamics and kinematics. This becomes of particular interest for modelling, estimation and control of mechanical systems......-known Euler-Poincaré reduction to a rigid body motion with forcing....
Euler-Poincaré Reduction of a Rigid Body Motion
DEFF Research Database (Denmark)
Wisniewski, Rafal; Kulczycki, P.
2004-01-01
. Assuming that the system possesses symmetry and the configuration manifold corresponds to a Lie group, the Euler-Poincaré reduction breaks up the motion into separate equations of dynamics and kinematics. This becomes of particular interest for modelling, estimation and control of mechanical systems......-known Euler-Poincaré reduction to a rigid body motion with forcing....
Euler-Poincare Reduction of a Rigid Body Motion
DEFF Research Database (Denmark)
Wisniewski, Rafal; Kulczycki, P.
2005-01-01
. Assuming that the system possesses symmetry and the configuration manifold corresponds to a Lie group, the Euler-Poincare reduction breaks up the motion into separate equations of dynamics and kinematics. This becomes of particular interest for modeling, estimation and control of mechanical systems......-known Euler-Poincare reduction to a rigid body motion with forcing....
Dynamics of Rigid Bodies and Flexible Beam Structures
DEFF Research Database (Denmark)
Nielsen, Martin Bjerre
of rigid bodies and flexible beam structures with emphasis on the rotational motion. The first part deals with motion in a rotating frame of reference. A novel approach where the equations of motion are formulated in a hybrid state-space in terms of local displacements and global velocities is presented...
Drawing the Free Rigid Body Dynamics According to Jacobi
Pina, Eduardo G
2015-01-01
Guided by the Jacobi's work published the year before his death about the rotation of a rigid body, the behavior of the rotation matrix describing the dynamics of the free rigid body is studied. To illustrate this dynamics one draws on a unit sphere the trace of the three unit vectors, in the body system along the principal directions of inertia. A minimal set of properties of Jacobi's elliptic functions are used, those which allow to compute with the necessary precision the dynamics of the rigid body without torques, the so called Euler's top. Emphasis is on the paper published by Jacobi in 1850 on the explicit expression for the components of the rotation matrix. The tool used to compute the trajectories to be drawn are the Jacobi's Fourier series for {\\sl theta} and {\\sl eta} functions with extremely fast convergence. The Jacobi's {\\sl sn}, {\\sl cn} and {\\sl dn} functions, which are better known, are used also as ratios of {\\sl theta} functions which permit quick and accurate computation. Finally the main ...
Zhao, Cheng-Gong; Wang, Cong; Wei, Ying-Jie; Zhang, Xiao-Shi
2015-12-01
An experimental study of the axisymmetric slender body underwater movement was conducted using high-speed photography technology. From the results of the experiment, the characteristics of cavitation and ballistic of the axisymmetric, including the formation, development, evolution and collapse of the cavity, are presented in the paper. The experimental results show that the axisymmetric slender body moves in a supercavity, and the slender body rotate in the supercavity on its head at the same time due to the perturbation of launching. The supercavity wall is transparent and smooth except the tail itself. The impact between the tail of slender body and supercavity wall resulted from the slender body's rotation is termed as tail- slap which is one way to keep the stabilization of the movement. Series of different flow mechanisms and the relationship between ballistic characteristics and cavity characteristics with defferent initial velocities are discussed. The slender bodies have different accelerations and ballistics with different initial velocity which means they have different drag forces.
A method for measuring the inertia properties of rigid bodies
Gobbi, M.; Mastinu, G.; Previati, G.
2011-01-01
A method for the measurement of the inertia properties of rigid bodies is presented. Given a rigid body and its mass, the method allows to measure (identify) the centre of gravity location and the inertia tensor during a single test. The proposed technique is based on the analysis of the free motion of a multi-cable pendulum to which the body under consideration is connected. The motion of the pendulum and the forces acting on the system are recorded and the inertia properties are identified by means of a proper mathematical procedure based on a least square estimation. After the body is positioned on the test rig, the full identification procedure takes less than 10 min. The natural frequencies of the pendulum and the accelerations involved are quite low, making this method suitable for many practical applications. In this paper, the proposed method is described and two test rigs are presented: the first is developed for bodies up to 3500 kg and the second for bodies up to 400 kg. A validation of the measurement method is performed with satisfactory results. The test rig holds a third part quality certificate according to an ISO 9001 standard and could be scaled up to measure the inertia properties of huge bodies, such as trucks, airplanes or even ships.
Impedance of rigid bodies in one-dimensional elastic collisions
Santos, Janilo; Nelson, Osman Rosso
2012-01-01
In this work we study the problem of one-dimensional elastic collisions of billiard balls, considered as rigid bodies, in a framework very different from the classical one presented in text books. Implementing the notion of impedance matching as a way to understand eficiency of energy transmission in elastic collisions, we find a solution which frames the problem in terms of this conception. We show that the mass of the ball can be seen as a measure of its impedance and verify that the problem of maximum energy transfer in elastic collisions can be thought of as a problem of impedance matching between different media. This approach extends the concept of impedance, usually associated with oscillatory systems, to system of rigid bodies.
A symmetric splitting method for rigid body dynamics
Directory of Open Access Journals (Sweden)
E. Celledoni
2006-04-01
Full Text Available It has been known since the time of Jacobi that the solution to the free rigid body (FRB equations of motion is given in terms of a certain type of elliptic functions. Using the Arithmetic-Geometric mean algorithm, (1, these functions can be calculated efficiently and accurately. The overall approach yields a faster and more accurate numerical solution to the FRB equations compared to standard numerical ODE and symplectic solvers. In this paper we investigate the possibility of extending this approach to the case of rigid bodies subject to external forces. By using a splitting strategy similar to the one proposed in (14, we decompose the vector field of our problem in a FRB problem and another completely integrable vector field. We apply the method to the simulation of the heavy top.
Rotating and rolling rigid bodies and the "hairy ball" theorem
Bormashenko, Edward; Kazachkov, Alexander
2017-06-01
Rotating and rolling rigid bodies exemplify a fascinating theorem of topology, jokingly called the "hairy ball" theorem, which demands that any continuous tangent vector field on the sphere has at least one point where the field is zero. We demonstrate via a gedanken experiment how drilling through a rotating ball, thereby converting it into a torus, leads to the elimination of zero-velocity points on the ball surface. Using the same reasoning, zero-velocity points can be removed from the surface of a drilled spinning top. We discuss the location of zero-velocity points on the surfaces of rigid bodies rolling with no slip and with slip. Observations made from different reference frames identify various zero-velocity points. Illustrative experiments visualizing zero-velocity points are presented.
Nonlinear dynamics mathematical models for rigid bodies with a liquid
Lukovsky, Ivan A
2015-01-01
This book is devoted to analytically approximate methods in the nonlinear dynamics of a rigid body with cavities partly filled by liquid. It combines several methods and compares the results with experimental data. It is useful for experienced and early-stage readers interested in analytical approaches to fluid-structure interaction problems, the fundamental mathematical background and modeling the dynamics of such complex mechanical systems.
A SYMPLECTIC ALGORITHM FOR DYNAMICS OF RIGID BODY
Institute of Scientific and Technical Information of China (English)
LU Ying-jie; REN Ge-xue
2006-01-01
For the dynamics of a rigid body with a fixed point based on the quaternion and the corresponding generalized momenta, a displacement-based symplectic integration scheme for differential-algebraic equations is proposed and applied to the Lagrange's equations based on dependent generalized momenta. Numerical experiments show that the algorithm possesses such characters as high precision and preserving system invariants.More importantly, the generalized momenta based Lagrange's equations show unique advantages over the traditional Lagrange's equations in symplectic integrations.
The power spectrum and correlation of flow noise for an axisymmetric body in water
Institute of Scientific and Technical Information of China (English)
Li Xue-Gang; Yang Kun-De; Wang Yong
2011-01-01
Understanding the physical features of the flow noise for an axisymmetric body is important for improving the performance of a sonar mounted on an underwater platform. Analytical calculation and numerical analysis of the physical features of the flow noise for an axisymmetric body are presented and a simulation scheme for the noise correlation on the hydrophones is given. It is shown that the numerical values of the flow noise coincide well with the analytical values. The main physical features of flow noise are obtained. The flow noises of two different models are compared and a model with a rather optimal fore-body shape is given. The flow noise in horizontal symmetry profile of the axisymmetric body is non-uniform, but it is omni-directional and has little difference in the cross section of the body. The loss of noise diffraction has a great effect on the flow noise from boundary layer transition. Meanwhile, based on the simulation, the noise power level increases with velocity to approximately the fifth power at high frequencies,which is consistent with the experiment data reported in the literature. Furthermore, the flow noise received by the acoustic array has lower correlation at a designed central frequency, which is important for sonar system design.
Kinematic approach in the impact problem of rigid bodies
Energy Technology Data Exchange (ETDEWEB)
Sinopoli, A. (I.U.A.V., Venezia (Italy))
1989-11-01
The aim of this work is to analyze, by means of a kinematic approach, the problem of the impact between rigid bodies, when the surfaces involved in the impulsive phenomenon are of finite extent. The formulation here adopted permits to use the Gauss variational principle of least compulsion and to formulate the dynamic evolution of the system, after an impact, as a minimization problem. In this case, among all the possible subsequent motions, the real one is that which minimizes the kinetic energy connected to the sudden velocities variations. Interesting results are obtained in the case of the impact between a rigid column (either monolithic or made of several blocks) and a rigid ground. In particular, it can be shown that if previous motion of a rigid block is a rotation around its base corner edge, the motion after the impact is either a rototranslation or merely a translation, depending on the dimensional ratio. In any case, the subsequent motion is characterized by a component of sliding, so that the impact plays the role of filter between the possible degrees of freedom of the system and, at the same time, determines a possible coupling between rotation and translation. This conclusion is a novelty with respect to the results obtained in other papers (4-6), where a classical approach for the impact has been adopted.
Identification of Helicopter Rigid Body Dynamics from Flight Data.
Directory of Open Access Journals (Sweden)
Jatinder Singh
1998-01-01
Full Text Available This paper discusses helicopter modelling and identification related aspects. By applying thesystem identification methodology, longitudinal and lateral-directional rigid body helicopter dynamics are identified from flight data. Aerodynamic parameters from single input excitation as wellas multimanoeuver evaluation are estimated utilising output-error approach. The formulatedmathematical models yield adequate fit to measured time histories. Results obtained from the proof-of-match for model validation indicate that the identified derivatives can satisfactorily predictlongitudinal dynamics to a given arbitrary input. It is further demonstrated for the present study thatlateral body dynamics can be adequately predicted by including cross-coupling terms in the estimation model.
Coordinating control of multiple rigid bodies based on motion primitives
Institute of Scientific and Technical Information of China (English)
Fan Wu; Zhi-Yong Geng
2012-01-01
This paper studies the problem of coordinated motion generation for a group of rigid bodies.Two classes of coordinated motion primitives,relative equilibria and maneuvers,are given as building blocks for generating coordinated motions.In a motion-primitive based planning framework,a control method is proposed for the robust execution of a coordinated motion plan in the presence of perturbations,The control method combines the relative equilibria stabilization with maneuver design,and results in a closeloop motion planning framework.The performance of the control method has been illustrated through a numerical simulation.
Control of the rigid body and dynamics with symmetry
Lum, Kai-Yew
This dissertation explores various problems in the control of the rigid body and related dynamical systems with symmetry, utilizing various modeling approaches and control techniques. We first derive a control law that asymptotically stabilizes an unbalanced top to the sleeping motion. We rewrite the classical Euler-Poisson equations by projecting the phase space onto IRsp5. The control law is based on the Hamilton-Jacobi-Bellman theory with zero dynamics and partial stability. Lyapunov techniques are used in the analysis. Next, the control of rotor imbalance with magnetic bearings is considered in the adaptive virtual autobalancing and adaptive autocentering approaches. We derive single-plane and two-plane balancing control algorithms that provide asymptotic estimates of the rotor imbalance, and that guarantee consistent performance under varying spin rate. These algorithms are based on emulation of the mechanical autobalancer. We discuss the theory based on linear analysis, and simulation and experimental results. We go on to investigate symmetry properties associated with mechanical control systems and certain nonlinear control systems. First, we generalize the classical Serret-Andoyer transformation for the free rigid body to left-invariant, hyperregular Hamiltonian systems on Tsp*SO(3), employing the notion of symplectic (Marsden-Weinstein) reduction. We then apply this result to the controlled rigid body, and show that for Hamiltonian controls that preserve the rigid body structure, the generalized Serret-Andoyer transformation yields a two dimensional representation of the closed-loop motion in canonical form. Applications to the stability analysis of relative equilibria and numerical integration are also discussed. Finally, we apply the concept of reduction to certain regulation problems on smooth manifolds. Following the works of Van der Schaft (1981) and Grizzle and Marcus (1985), we show that an output feedback regulation problem possessing certain
Impedance of rigid bodies in one-dimensional elastic collisions
Santos, Janilo; de Oliveira, Bruna P. W.; Nelson,Osman Rosso
2012-01-01
In this work we study the problem of one-dimensional elastic collisions of billiard balls, considered as rigid bodies, in a framework very different from the classical one presented in text books. Implementing the notion of impedance matching as a way to understand efficiency of energy transmission in elastic collisions, we find a solution which frames the problem in terms of this conception. We show that the mass of the ball can be seen as a measure of its impedance and verify that the probl...
Dynamic Buckling of Column Impacted by a Rigid Body
Institute of Scientific and Technical Information of China (English)
Zhijun Han; Hongwei Ma; Shanyuan Zhang
2004-01-01
The dynamic buckling of an elastic column subjected to axial impact by a rigid body is discussed in accordance with the energy law in this paper. The equation of lateral disturbance used to analysis the problem is developed by taking into account the effect of stress wave. The power series solution of this problem has been obtained by using the power series approach. The buckling criterion of this problem is proposed by analyzing the characteristics of the solution. The relationships between critical velocity and impacting mass as well as critical velocity and critical length are given by using theoretical analysis and numerical computation.
The free rigid body dynamics: Generalized versus classic
Tudoran, Rǎzvan M.
2013-07-01
In this paper we analyze some normal forms of a general quadratic Hamiltonian system defined on the dual of the Lie algebra {o}(K) of real K-skew-symmetric matrices, where K is an arbitrary 3×3 real symmetric matrix. A consequence of the main results is that any first-order autonomous three-dimensional differential equation possessing two independent quadratic constants of motion, which admit a positive/negative definite linear combination, is affinely equivalent to the classical "relaxed" free rigid body dynamics with linear control parameters.
MacCallum, M A H; Vera, R; Callum, Malcolm A.H. Mac; Mars, Marc; Vera, Ra\\"ul
2006-01-01
Perturbed stationary axisymmetric isolated bodies, e.g. stars, represented by a matter-filled interior and an asymptotically flat vacuum exterior joined at a surface where the Darmois matching conditions are satisfied, are considered. The initial state is assumed to be static. The perturbations of the matching conditions are derived and used as boundary conditions for the perturbed Ernst equations in the exterior region. The perturbations are calculated to second order. The boundary conditions are overdetermined: necessary and sufficient conditions for their compatibility are derived. The special case of perturbations of spherical bodies is given in detail.
Collisions of Constrained Rigid Body Systems with Friction
Directory of Open Access Journals (Sweden)
Haijun Shen
1998-01-01
Full Text Available A new approach is developed for the general collision problem of two rigid body systems with constraints (e.g., articulated systems, such as massy linkages in which the relative tangential velocity at the point of contact and the associated friction force can change direction during the collision. This is beyond the framework of conventional methods, which can give significant and very obvious errors for this problem, and both extends and consolidates recent work. A new parameterization and theory characterize if, when and how the relative tangential velocity changes direction during contact. Elastic and dissipative phenomena and different values for static and kinetic friction coefficients are included. The method is based on the explicitly physical analysis of events at the point of contact. Using this method, Example 1 resolves (and corrects a paradox (in the literature of the collision of a double pendulum with the ground. The method fundamentally subsumes other recent models and the collision of rigid bodies; it yields the same results as conventional methods when they would apply (Example 2. The new method reformulates and extends recent approaches in a completely physical context.
Computational Fluid Dynamics Demonstration of Rigid Bodies in Motion
Camarena, Ernesto; Vu, Bruce T.
2011-01-01
The Design Analysis Branch (NE-Ml) at the Kennedy Space Center has not had the ability to accurately couple Rigid Body Dynamics (RBD) and Computational Fluid Dynamics (CFD). OVERFLOW-D is a flow solver that has been developed by NASA to have the capability to analyze and simulate dynamic motions with up to six Degrees of Freedom (6-DOF). Two simulations were prepared over the course of the internship to demonstrate 6DOF motion of rigid bodies under aerodynamic loading. The geometries in the simulations were based on a conceptual Space Launch System (SLS). The first simulation that was prepared and computed was the motion of a Solid Rocket Booster (SRB) as it separates from its core stage. To reduce computational time during the development of the simulation, only half of the physical domain with respect to the symmetry plane was simulated. Then a full solution was prepared and computed. The second simulation was a model of the SLS as it departs from a launch pad under a 20 knot crosswind. This simulation was reduced to Two Dimensions (2D) to reduce both preparation and computation time. By allowing 2-DOF for translations and 1-DOF for rotation, the simulation predicted unrealistic rotation. The simulation was then constrained to only allow translations.
The computation of thick axisymmetric boundary layers and wakes around bodies of revolution
Markatos, N. C.
The paper is concerned with the computational investigation of thick, axisymmetric, turbulent boundary layers and wakes around bodies of revolution. The procedures employed take full account of the influence of longitudinal and transverse surface curvatures and normal pressure gradients on the development of the boundary layer and wake, and also the viscous-inviscid interaction in the tail region of the body. The method makes it possible to calculate the static pressure and the velocity profiles along the body as well as the drag components; and it is applicable to both two- and three-dimensional situations, enabling, for example, the prediction of flows around ships' and submarines' hulls to be made. The application of the fully-elliptic calculation procedure to a body of revolution is described, and comparisons made between predictions and experimental measurements. The calculated axial variation of skin friction and pressure coefficient, and the velocity profiles are shown to be in fair agreement with experimental values.
Unifying Rigid and Soft Bodies Representation: The Sulfur Physics Engine
Directory of Open Access Journals (Sweden)
Dario Maggiorini
2014-01-01
Full Text Available Video games are (also real-time interactive graphic simulations: hence, providing a convincing physics simulation for each specific game environment is of paramount importance in the process of achieving a satisfying player experience. While the existing game engines appropriately address many aspects of physics simulation, some others are still in need of improvements. In particular, several specific physics properties of bodies not usually involved in the main game mechanics (e.g., properties useful to represent systems composed by soft bodies, are often poorly rendered by general-purpose engines. This issue may limit game designers when imagining innovative and compelling video games and game mechanics. For this reason, we dug into the problem of appropriately representing soft bodies. Subsequently, we have extended the approach developed for soft bodies to rigid ones, proposing and developing a unified approach in a game engine: Sulfur. To test the engine, we have also designed and developed “Escape from Quaoar,” a prototypal video game whose main game mechanic exploits an elastic rope, and a level editor for the game.
Dynamics of parallel robots from rigid bodies to flexible elements
Briot, Sébastien
2015-01-01
This book starts with a short recapitulation on basic concepts, common to any types of robots (serial, tree structure, parallel, etc.), that are also necessary for computation of the dynamic models of parallel robots. Then, as dynamics requires the use of geometry and kinematics, the general equations of geometric and kinematic models of parallel robots are given. After, it is explained that parallel robot dynamic models can be obtained by decomposing the real robot into two virtual systems: a tree-structure robot (equivalent to the robot legs for which all joints would be actuated) plus a free body corresponding to the platform. Thus, the dynamics of rigid tree-structure robots is analyzed and algorithms to obtain their dynamic models in the most compact form are given. The dynamic model of the real rigid parallel robot is obtained by closing the loops through the use of the Lagrange multipliers. The problem of the dynamic model degeneracy near singularities is treated and optimal trajectory planning for cro...
Leonhard Euler and the mechanics of rigid bodies
Marquina, J. E.; Marquina, M. L.; Marquina, V.; Hernández-Gómez, J. J.
2017-01-01
In this work we present the original ideas and the construction of the rigid bodies theory realised by Leonhard Euler between 1738 and 1775. The number of treatises written by Euler on this subject is enormous, including the most notorious Scientia Navalis (1749), Decouverte d’un noveau principe de mecanique (1752), Du mouvement de rotation des corps solides autour d’un axe variable (1765), Theoria motus corporum solidorum seu rigidorum (1765) and Nova methodus motu corporum rigidorum determinandi (1776), in which he developed the ideas of the instantaneous rotation axis, the so-called Euler equations and angles, the components of what is now known as the inertia tensor, the principal axes of inertia, and, finally, the generalisation of the translation and rotation movement equations for any system. Euler, the man who ‘put most of mechanics into its modern form’ (Truesdell 1968 Essays in the History of Mechanics (Berlin: Springer) p 106).
Transitions to chaos in the wake of an axisymmetric bluff body
Energy Technology Data Exchange (ETDEWEB)
Bury, Yannick, E-mail: yannick.bury@isae.fr [Université de Toulouse, ISAE, 10, avenue Edouard Belin, 31055 Toulouse (France); Jardin, Thierry, E-mail: thierry.jardin@isae.fr [Université de Toulouse, ISAE, 10, avenue Edouard Belin, 31055 Toulouse (France)
2012-10-01
This Letter aims at understanding the dynamical process that leads to the onset of chaos in the flow past a blunt-based axisymmetric bluff body. On the basis of direct numerical simulations, conducted for Reynolds numbers ranging from 100 to 900, we show that the flow undergoes multiple transitions, successively giving rise to the SS, RSP{sub a}, RSP{sub b}, RSP{sub c} and RSB wake states. In particular, the RSP{sub c} state, revealed in this work via long-term computations, is characterized by intermittent vortex stretching denoting the onset of chaos before the symmetry breaking and the occurrence of the RSB state. -- Highlights: ► We performed long-term Direct Numerical Simulations of the flow past an axisymmetric bluff body. ► We reveal the existence of a new wake mode. ► We show that this mode triggers chaos before the loss of planar symmetry in the wake. ► We decipher the transitions leading to this mode through the description of the wake structures.
Hamiltonian Dynamics of Several Rigid Bodies Interacting with Point Vortices
Weißmann, Steffen
2014-04-01
We derive the dynamics of several rigid bodies of arbitrary shape in a two-dimensional inviscid and incompressible fluid, whose vorticity is given by point vortices. We adopt the idea of Vankerschaver et al. (J. Geom. Mech. 1(2): 223-226, 2009) to derive the Hamiltonian formulation via symplectic reduction from a canonical Hamiltonian system. The reduced system is described by a noncanonical symplectic form, which has previously been derived for a single circular disk using heavy differential-geometric machinery in an infinite-dimensional setting. In contrast, our derivation makes use of the fact that the dynamics of the fluid, and thus the point vortex dynamics, is determined from first principles. Using this knowledge we can directly determine the dynamics on the reduced, finite-dimensional phase space, using only classical mechanics. Furthermore, our approach easily handles several bodies of arbitrary shape. From the Hamiltonian description we derive a Lagrangian formulation, which enables the system for variational time integrators. We briefly describe how to implement such a numerical scheme and simulate different configurations for validation.
Yamauchi, G.; Johnson, W.
1984-01-01
A computationally efficient body analysis designed to couple with a comprehensive helicopter analysis is developed in order to calculate the body-induced aerodynamic effects on rotor performance and loads. A modified slender body theory is used as the body model. With the objective of demonstrating the accuracy, efficiency, and application of the method, the analysis at this stage is restricted to axisymmetric bodies at zero angle of attack. By comparing with results from an exact analysis for simple body shapes, it is found that the modified slender body theory provides an accurate potential flow solution for moderately thick bodies, with only a 10%-20% increase in computational effort over that of an isolated rotor analysis. The computational ease of this method provides a means for routine assessment of body-induced effects on a rotor. Results are given for several configurations that typify those being used in the Ames 40- by 80-Foot Wind Tunnel and in the rotor-body aerodynamic interference tests being conducted at Ames. A rotor-hybrid airship configuration is also analyzed.
Knowledge-i-action: an example with rigid body motion
Salvador Cabral da Costa, Sayonara; Moreira, Marco Antonio
2005-01-01
This paper reports the analysis of the resolution of a paper-and-pencil problem, by eight undergraduate students majoring in engineering (six) and physics (two) at the Pontifícia Universidade Católica do Rio Grande do Sul, in Porto Alegre, Brazil. The problem concerns kinetics of a rigid body, and the analysis was done in the light of Johnson-Laird’s mental models theory and Vergnaud’s conceptual fields theory. The problem-solving process has been investigated from the presentation of the problems’ variables and the pictures that followed it, up to the resolution itself. This investigation was carried out by analysing the knowledge-in-action that students have used as inferred from their written solutions and from what they said in semi-structured interviews. The findings of this analysis identified some characteristics in their answers that may help us to understand the processes used by students during the problem-solving task, with possible consequences for classroom procedures used by teachers.
A new cantilever beam-rigid-body MEMS gyroscope: mathematical model and linear dynamics
Lajimi, Seyed Amir Mousavi; Abdel-Rahman, Eihab
2014-01-01
A new microbeam-rigid-body gyroscope is introduced and its static and dynamic behaviours are studied. The main structure includes a microbeam and an eccentric end-rigid-body influencing the dynamic and static characteristics of the sensor. The sensitivity of the device and the effect of system parameters on the microsystem's response are investigated.
THE FLUCTUATION CHARACTERISTICS OF NATURAL AND VENTILATED CAVITIES ON AN AXISYMMETRIC BODY
Institute of Scientific and Technical Information of China (English)
FENG Xue-mei; LU Chuan-jing; HU Tian-qun; WU Lei; LI Jie
2005-01-01
Natural and ventilated cavitations generated on a smooth-nosed axisymmetric body were studied experimental-ly. The characteristics of small scale and localized fluctuations of "steady cavities" were measured by pressure transducers. Comparisons between natural and ventilated cavities at differ-ent measured points for several cavitation numbers were done. It was observed that the dominant fluctuations were concen-trated in the frequency range of OHz-50Hz for all the cavitati-on cases, Similar shapes and magnitudes of the frequency spectra were detected for both natural and ventilated cavities. Much larger spectral amplitude in the cavity closure region suggested as fluctuations source. From partial cavitating flow to supercavitating flow, the dominat frequency and the corre-sponding amplitude decreased with decrasing cavitation num-ber, which meant that cavity became more steady while devel-oping.
Experimental Investigation on Cavitating Flow Shedding over an Axisymmetric Blunt Body
Institute of Scientific and Technical Information of China (English)
HU Changli; WANG Guoyu; HUANG Biao
2015-01-01
Nowadays, most researchers focus on the cavity shedding mechanisms of unsteady cavitating flows over different objects, such as 2D/3D hydrofoils, venturi-type section, axisymmetric bodies with different headforms, and so on. But few of them pay attention to the differences of cavity shedding modality under different cavitation numbers in unsteady cavitating flows over the same object. In the present study, two kinds of shedding patterns are investigated experimentally. A high speed camera system is used to observe the cavitating flows over an axisymmetric blunt body and the velocity fields are measured by a particle image velocimetry (PIV) technique in a water tunnel for different cavitation conditions. The U-type cavitating vortex shedding is observed in unsteady cavitating flows. When the cavitation number is 0.7, there is a large scale cavity rolling up and shedding, which cause the instability and dramatic fluctuation of the flows, while at cavitation number of 0.6, the detached cavities can be conjunct with the attached part to induce the break-off behavior again at the tail of the attached cavity, as a result, the final shedding is in the form of small scale cavity and keeps a relatively steady flow field. It is also found that the interaction between the re-entrant flow and the attached cavity plays an important role in the unsteady cavity shedding modality. When the attached cavity scale is insufficient to overcome the re-entrant flow, it deserves the large cavity rolling up and shedding just as that at cavitation number of 0.7. Otherwise, the re-entrant flow is defeated by large enough cavity to induce the cavity-combined process and small scale cavity vortexes shedding just as that of the cavitation number of 0.6. This research shows the details of two different cavity shedding modalities which is worthful and meaningful for the further study of unsteady cavitation.
Distributed forcing of the flow past a blunt-based axisymmetric bluff body
Jardin, Thierry; Bury, Yannick
2014-06-01
In this paper, we address the influence of a blowing-/suction-type distributed forcing on the flow past a blunt-based axisymmetric bluff body by means of direct numerical simulations. The forcing is applied via consecutive blowing and suction slots azimuthally distributed along the trailing edge of the bluff body. We examine the impact of the forcing wavelength, amplitude and waveform on the drag experienced by the bluff body and on the occurrence of the reflectional symmetry preserving and reflectional symmetry breaking wake modes, for Reynolds numbers 800 and 1,000. We show that forcing the flow at wavelengths inherent to the unforced flow drastically damps drag oscillations associated with the vortex shedding and vorticity bursts, up to their complete suppression. The overall parameter analysis suggests that this damping results from the surplus of streamwise vorticity provided by the forcing that tends to stabilize the ternary vorticity lobes observed at the aft part of the bluff body. In addition, conversely to a blowing-type or suction-type forcing, the blowing-/suction-type forcing involves strong nonlinear interactions between locally decelerated and accelerated regions, severely affecting both the mean drag and the frequencies representative of the vortex shedding and vorticity bursts.
Assumptions and Axioms: Mathematical Structures to Describe the Physics of Rigid Bodies
Butler, Philip H; Renaud, Peter F
2010-01-01
This paper challenges some of the common assumptions underlying the mathematics used to describe the physical world. We start by reviewing many of the assumptions underlying the concepts of real, physical, rigid bodies and the translational and rotational properties of such rigid bodies. Nearly all elementary and advanced texts make physical assumptions that are subtly different from ours, and as a result we develop a mathematical description that is subtly different from the standard mathematical structure. Using the homogeneity and isotropy of space, we investigate the translational and rotational features of rigid bodies in two and three dimensions. We find that the concept of rigid bodies and the concept of the homogeneity of space are intrinsically linked. The geometric study of rotations of rigid objects leads to a geometric product relationship for lines and vectors. By requiring this product to be both associative and to satisfy Pythagoras' theorem, we obtain a choice of Clifford algebras. We extend o...
Kinematic simulation of human gait with a multi-rigid-body foot model
Institute of Scientific and Technical Information of China (English)
YANG Yan; HU Xiaochun; LI Xiaopeng
2012-01-01
The paper builds a multi-rigid-body model of human with a 4-rigid-body foot in the 3D CAD software Solidworks, based on human anatomy. By controlling the rotation of the ankle and major joints of human body while walking, the Kinematic simulation was performed in the dynamics simulation software ADAMS. The paper analyzes the simulate results and points out deficiencies in the current work and the direction of research efforts in future.
Cavitation studies on axi-symmetric underwater body with pumpjet propulsor in cavitation tunnel
Directory of Open Access Journals (Sweden)
Ch. Suryanarayana
2010-12-01
Full Text Available A pumpjet propulsor (PJP was designed for an underwater body (UWB with axi-symmetric configuration. Its performance was predicted through CFD study and models were manufactured. The propulsor design was evaluated for its propulsion characteristics through model tests conducted in a Wind Tunnel (WT. In the concluding part of the study, evaluation of the cavitation performance of the pumpjet was undertaken in a cavitation tunnel (CT. In order to assess the cavitation free operation speeds and depths of the body, cavitation tests of the PJP were carried out in behind condition to determine the inception cavitation numbers for rotor, stator and cowl. The model test results obtained were corrected for full scale Reynolds number and subsequently analyzed for cavitation inception speeds at different operating depths. From model tests it was also found that the cavitation inception of the rotor takes place on the tip face side at higher advance ratios and cavitation shifts towards the suction side as the RPS increases whereas the stator and cowl are free from cavitation.
Measurements in the flow around a marine propeller at the stern of an axisymmetric body
Hyun, B.-S.; Patel, V. C.
1991-04-01
An experimental study of the flow around and behind an axisymmetric body driven by a marine propeller is reported. Experiments were performed in a wind tunnel to document this complex, unsteady, three-dimensional, turbulent shear flow. Measurements were made in the boundary layer and wake of the bare body with a fixed dummy hub for the propeller, with the dummy hub rotating, and finally, with the propeller in operation. A five-hole yaw probe was employed for the mean-flow measurements, and two- and threesensor hotwires were used to obtained the mean and turbulent velocity fields. Part 1 of this two-part paper describes the experimental arrangement and circumferentially-averaged results which clarify certain overall aspects of the flow when it is viewed as a rotationally-symmetric flow. These are of special interest in marine hydrodynamics. In Part 2, the triple-sensor hotwire data are analyzed using phase-averaging techniques to reconstruct the instantaneous velocity and Reynolds-stress fields downstream of the propeller to show the evolution of the wakes of individual blades, blade-tip vortices, and the complex flow associated with vortices generated at hub-blade junctions.
Asymmetric steady streaming as a mechanism for acoustic propulsion of rigid bodies
Nadal, Francois
2014-01-01
Recent experiments showed that standing acoustic waves could be exploited to induce self-propulsion of rigid metallic particles in the direction perpendicular to the acoustic wave. We propose in this paper a physical mechanism for these observations based on the interplay between inertial forces in the fluid and the geometrical asymmetry of the particle shape. We consider an axisymmetric rigid near-sphere oscillating in a quiescent fluid along a direction perpendicular to its symmetry axis. The kinematics of oscillations can be either prescribed or can result dynamically from the presence of an external oscillating velocity field. Steady streaming in the fluid, the inertial rectification of the time-periodic oscillating flow, generates steady stresses on the particle which, in general, do not average to zero, resulting in a finite propulsion speed along the axis of the symmetry of the particle and perpendicular to the oscillation direction. Our derivation of the propulsion speed is obtained at leading order i...
Experimental evaluation of pumpjet propulsor for an axisymmetric body in wind tunnel
Directory of Open Access Journals (Sweden)
Ch. Suryanarayana
2010-03-01
Full Text Available Design of a Pump Jet Propulsor (PJP was undertaken for an underwater body with axisymmetric configuration using axial flow compressor design techniques supported by Computational Fluid Dynamics (CFD analysis for performance prediction. Experimental evaluation of the PJP was carried out through experiments in a Wind Tunnel Facility (WTF using momentum defect principle for propulsive performance prior to proceeding with extensive experimental evaluation in towing tank and cavitation tunnel. Experiments were particularly conducted with respect to Self Propulsion Point (SPP, residual torque and thrust characteristics over a range of vehicle advance ratio in order to ascertain whether sufficient thrust is developed at the design condition with least possible imbalance torque left out due to residual swirl in the slip stream. Pumpjet and body models were developed for the propulsion tests using Aluminum alloy forged material. Tests were conducted from 0 m/s to 30 m/s at four rotational speeds of the PJP. SPP was determined confirming the thrust development capability of PJP. Estimation of residual torque was carried out at SPP corresponding to speeds of 15, 20 and 25 m/s to examine the effectiveness of the stator. Estimation of thrust and residual torque was also carried out at wind speeds 0 and 6 m/s for PJP RPMs corresponding to self propulsion tests to study the propulsion characteristics during the launch of the vehicle in water where advance ratios are close to Zero. These results are essential to assess the thrust performance at very low advance ratios to accelerate the body and to control the body during initial stages. This technique has turned out to be very useful and economical method for quick assessment of overall performance of the propulsor and generation of exhaustive fluid dynamic data to validate CFD techniques employed.
Augmented Eigenvector and Its Orthogonality of Linear Multi-rigid-flexibel-body System
Institute of Scientific and Technical Information of China (English)
RUI Xiao-ting; YUN Lai-feng; WANG Guo-ping; LU Yu-qi
2008-01-01
The orthogonality of eigenvector is a precondition to compute the dynamic responses of linear multi-rigid-flexible-body system using the classical modal analysis method. For a linear multi-rigid-flexible-body system, the eigenfunction does not satisfy the orthogonality under ordinary meaning. A new concept--augmented eigenvector is introduced, which is used to overcome the orthogonality problem of eigenvectors of linear multi-rigid-flexible-body system. The constitution method and the orthogonality of augmented eigenvector are expatiated. After the orthogonality of augmented eigenvector is acquired, the coupling of coordinates in dynamics equations can be released, which makes it possible to analyze exactly the dynamic responses of linear multi-rigid-flexible-body system using the classical modal analysis method.
Contact point generation for convex polytopes in interactive rigid body dynamics
DEFF Research Database (Denmark)
Silcowitz-Hansen, Morten; Abel, Sarah Maria Niebe; Erleben, Kenny
When computing contact forces in rigid body dynamics systems, most state-of-the-art solutions use iterative methods such as the projected Gauss–Seidel (PGS) method. Methods such as the PGS method are preferred for their robustness. However, the time-critical nature of interactive applications...... for convex polytopes. A novel contact point generation method is presented, which is based on growth distances and Gauss maps. We demonstrate improvements when using our method in the context of interactive rigid body simulation...
Eigenvalues of an axially loaded cantilever beam with an eccentric end rigid body
Lajimi, S Amir Mousavi
2014-01-01
An analytical form of the characteristic equation for a vertically mounted cantilever beam with an end rigid body is obtained and solved for the eigenvalues of the structure. The effect of the weight of the structure is taken into consideration by estimating the load as a function of the length of the beam. The mass, rotary inertia and eccentricity of the end rigid body are demonstrated to considerably affect the eigenvalues of the structure.
NUMERICAL STUDY OF FLOW PAST AN AXISYMMETRIC BODY WITH A RING WING AT VARIOUS ATTACK ANGLES
Institute of Scientific and Technical Information of China (English)
Ren An-lu; Zou Jian-feng; Dai Zhi-qian
2003-01-01
The laminar and turbulent flows past an axisymmetric body with a ring wing were investigated numerically at various attack angles (0°-20°) for the Reynolds numbers ranging from 103 to 107. The DDM (Domain Decomposition Method) with the Schwarz iterative method based on finite difference approximation was applied to simulate this problem. The primitive variable formulation was used for the solution of the incompressible Navier-Stoke equations. The velocity field was calculated from the unsteady momentum equation by marching in time. The continuity equation was replaced by a Poisson-type equation for the pressure with the Neumann boundary conditions. The Baldwin-Lomax model was adopted to simulate turbulence effect. The leap frog implicit iterative method was used for the time difference approximations. The computed pressure at the front stagnation point is found to have a small deviation, less than 10%, from the theoretical value. The outlet flux has a loss about 5%. The lift coefficients increase linearly with the attack angle, but for attack angles greater than 15° the lift coefficients show mild decrease. The friction drag coefficients are insensitive to the attack angles, but the pressure drag coefficients increase markedly with the attack angles. In addition, complex flow patterns are revealed within the vicinity of the ring wing.
Hamilton, H. H., II; Spall, J. R.
1986-01-01
A time-asymptotic method has been used to obtain steady-flow solutions for axisymmetric inviscid flow over several blunt bodies including spheres, paraboloids, ellipsoids, and spherically blunted cones. Comparisons with experimental data and results of other computational methods have demonstrated that accurate solutions can be obtained using this approach. The method should prove useful as an analysis tool for comparing with experimental data and for making engineering calculations for blunt reentry vehicles.
Khuri, Marcus
2016-01-01
We establish inequalities relating the size of a material body to its mass, angular momentum, and charge, within the context of axisymmetric initial data sets for the Einstein equations. These inequalities hold in general without the assumption of the maximal condition, and use a notion of size which is easily computable. Moreover, these results give rise to black hole existence criteria which are meaningful even in the time-symmetric case, and also include certain boundary effects.
Evolution of motions of a rigid body about its center of mass
Chernousko, Felix L; Leshchenko, Dmytro D
2017-01-01
The book presents a unified and well-developed approach to the dynamics of angular motions of rigid bodies subjected to perturbation torques of different physical nature. It contains both the basic foundations of the rigid body dynamics and of the asymptotic method of averaging. The rigorous approach based on the averaging procedure is applicable to bodies with arbitrary ellopsoids of inertia. Action of various perturbation torques, both external (gravitational, aerodynamical, solar pressure) and internal (due to viscous fluid in tanks, elastic and visco-elastic properties of a body) is considered in detail. The book can be used by researchers, engineers and students working in attitude dynamics of spacecraft.
Mouse whole-body organ mapping by non-rigid registration approach
Xiao, Di; Zahra, David; Bourgeat, Pierrick; Berghofer, Paula; Acosta Tamayo, Oscar; Green, Heather; Gregoire, Marie Claude; Salvado, Olivier
2011-03-01
Automatic small animal whole-body organ registration is challenging because of subject's joint structure, posture and position difference and loss of reference features. In this paper, an improved 3D shape context based non-rigid registration method is applied for mouse whole-body skeleton registration and lung registration. A geodesic path based non-rigid registration method is proposed for mouse torso skin registration. Based on the above registration methods, a novel non-rigid registration framework is proposed for mouse whole-body organ mapping from an atlas to new scanned CT data. A preliminary experiment was performed to test the method on lung and skin registration. A whole-body organ mapping was performed on three target data and the selected organs were compared with the manual outlining results. The robust of the method has been demonstrated.
Projected Gauss-Seidel subspace minimization method for interactive rigid body dynamics
DEFF Research Database (Denmark)
Silcowitz-Hansen, Morten; Abel, Sarah Maria Niebe; Erleben, Kenny
2010-01-01
In interactive physical simulation, contact forces are applied to prevent rigid bodies from penetrating and to control slipping between bodies. Accurate contact force determination is a computationally hard problem. Thus, in practice one trades accuracy for performance. This results in visual...
A constrained generalised-α method for coupling rigid parallel chain kinematics and elastic bodies
Gransden, D.I.; Burkhard Bornemann, P.; Rose, M.; Nitzsche, F.
2015-01-01
A problem arises from combining flexible rotorcraft blades with stiffer mechanical links, which form a parallel kinematic chain. This paper introduces a method for solving index-3 differential algebraic equations for coupled stiff and elastic body systems with closed-loop kinematics. Rigid body dyna
A constrained generalised-α method for coupling rigid parallel chain kinematics and elastic bodies
Gransden, D.I.; Burkhard Bornemann, P.; Rose, M.; Nitzsche, F.
2015-01-01
A problem arises from combining flexible rotorcraft blades with stiffer mechanical links, which form a parallel kinematic chain. This paper introduces a method for solving index-3 differential algebraic equations for coupled stiff and elastic body systems with closed-loop kinematics. Rigid body
Separating brain motion into rigid body displacement and deformation under low-severity impacts.
Zou, Hong; Schmiedeler, James P; Hardy, Warren N
2007-01-01
The relative motion of the brain with respect to the skull has been widely studied to investigate brain injury mechanisms under impacts, but the motion patterns are not yet thoroughly understood. This work analyzes brain motion patterns using the most recent and advanced experimental relative brain/skull motion data collected under low-severity impacts. With a minimum total pseudo-strain energy, the closed-form solutions for rigid body translation and rotation were obtained by matching measured neutral density target (NDT) positions with initial NDT positions. The brain motion was thus separated into rigid body displacement and deformation. The results show that the brain has nearly pure rigid body displacement at low impact speed. As the impact becomes more severe, the increased brain motion primarily is due to deformation, while the rigid body displacement is limited in magnitude for both translation and rotation. Under low-severity impacts in the sagittal plane, the rigid body brain translation has a magnitude of 4-5 mm, and the whole brain rotation is on the order of +/-5 degrees.
Simulation Methods in the Contact with Impact of Rigid Bodies
Directory of Open Access Journals (Sweden)
Cristina Basarabă-Opritescu
2007-10-01
Full Text Available The analysis of impacts of elastic bodies is topical and it has many applications, practical and theoretical, too. The elastic character of collision is put in evidence, especially by the velocities of some parts of a particular body, named “ring”. In the presented paper, the situation of elastic collisions is put in evidence by the simulation with the help of the program ANSYS and it refers to the particular case of the ring, with the mechanical characteristics, given in the paper
Rigid body motion analysis system for off-line processing of time-coded video sequences
Snow, Walter L.; Shortis, Mark R.
1995-09-01
Photogrammetry affords the only noncontact means of providing unambiguous six-degree-of- freedom estimates for rigid body motion analysis. Video technology enables convenient off- the-shelf capability for obtaining and storing image data at frame (30 Hz) or field (60 Hz) rates. Videometry combines these technologies with frame capture capability accessible to PCs to allow unavailable measurements critical to the study of rigid body dynamics. To effectively utilize this capability, however, some means of editing, post processing, and sorting substantial amounts of time coded video data is required. This paper discusses a prototype motion analysis system built around PC and video disk technology, which is proving useful in exploring applications of these concepts to rigid body tracking and deformation analysis. Calibration issues and user interactive software development associated with this project will be discussed, as will examples of measurement projects and data reduction.
Estimating the orientation of a rigid body moving in space using inertial sensors
Energy Technology Data Exchange (ETDEWEB)
He, Peng, E-mail: peng.he.1@ulaval.ca; Cardou, Philippe, E-mail: pcardou@gmc.ulaval.ca [Université Laval, Robotics Laboratory, Department of Mechanical Engineering (Canada); Desbiens, André, E-mail: andre.desbiens@gel.ulaval.ca [Université Laval, Department of Electrical and Computer Engineering (Canada); Gagnon, Eric, E-mail: Eric.Gagnon@drdc-rddc.gc.ca [RDDC Valcartier (Canada)
2015-09-15
This paper presents a novel method of estimating the orientation of a rigid body moving in space from inertial sensors, by discerning the gravitational and inertial components of the accelerations. In this method, both a rigid-body kinematics model and a stochastic model of the human-hand motion are formulated and combined in a nonlinear state-space system. The state equation represents the rigid body kinematics and stochastic model, and the output equation represents the inertial sensor measurements. It is necessary to mention that, since the output equation is a nonlinear function of the state, the extended Kalman filter (EKF) is applied. The absolute value of the error from the proposed method is shown to be less than 5 deg in simulation and in experiments. It is apparently stable, unlike the time-integration of gyroscope measurements, which is subjected to drift, and remains accurate under large accelerations, unlike the tilt-sensor method.
Virtual rigid body: a new optical tracking paradigm in image-guided interventions
Cheng, Alexis; Lee, David S.; Deshmukh, Nishikant; Boctor, Emad M.
2015-03-01
Tracking technology is often necessary for image-guided surgical interventions. Optical tracking is one the options, but it suffers from line of sight and workspace limitations. Optical tracking is accomplished by attaching a rigid body marker, having a pattern for pose detection, onto a tool or device. A larger rigid body results in more accurate tracking, but at the same time large size limits its usage in a crowded surgical workspace. This work presents a prototype of a novel optical tracking method using a virtual rigid body (VRB). We define the VRB as a 3D rigid body marker in the form of pattern on a surface generated from a light source. Its pose can be recovered by observing the projected pattern with a stereo-camera system. The rigid body's size is no longer physically limited as we can manufacture small size light sources. Conventional optical tracking also requires line of sight to the rigid body. VRB overcomes these limitations by detecting a pattern projected onto the surface. We can project the pattern onto a region of interest, allowing the pattern to always be in the view of the optical tracker. This helps to decrease the occurrence of occlusions. This manuscript describes the method and results compared with conventional optical tracking in an experiment setup using known motions. The experiments are done using an optical tracker and a linear-stage, resulting in targeting errors of 0.38mm+/-0.28mm with our method compared to 0.23mm+/-0.22mm with conventional optical markers. Another experiment that replaced the linear stage with a robot arm resulted in rotational errors of 0.50+/-0.31° and 2.68+/-2.20° and the translation errors of 0.18+/-0.10 mm and 0.03+/-0.02 mm respectively.
Computing the Free Energy along a Reaction Coordinate Using Rigid Body Dynamics.
Tao, Peng; Sodt, Alexander J; Shao, Yihan; König, Gerhard; Brooks, Bernard R
2014-10-14
The calculations of potential of mean force along complex chemical reactions or rare events pathways are of great interest because of their importance for many areas in chemistry, molecular biology, and material science. The major difficulty for free energy calculations comes from the great computational cost for adequate sampling of the system in high-energy regions, especially close to the reaction transition state. Here, we present a method, called FEG-RBD, in which the free energy gradients were obtained from rigid body dynamics simulations. Then the free energy gradients were integrated along a reference reaction pathway to calculate free energy profiles. In a given system, the reaction coordinates defining a subset of atoms (e.g., a solute, or the quantum mechanics (QM) region of a quantum mechanics/molecular mechanics simulation) are selected to form a rigid body during the simulation. The first-order derivatives (gradients) of the free energy with respect to the reaction coordinates are obtained through the integration of constraint forces within the rigid body. Each structure along the reference reaction path is separately subjected to such a rigid body simulation. The individual free energy gradients are integrated along the reference pathway to obtain the free energy profile. Test cases provided demonstrate both the strengths and weaknesses of the FEG-RBD method. The most significant benefit of this method comes from the fast convergence rate of the free energy gradient using rigid-body constraints instead of restraints. A correction to the free energy due to approximate relaxation of the rigid-body constraint is estimated and discussed. A comparison with umbrella sampling using a simple test case revealed the improved sampling efficiency of FEG-RBD by a factor of 4 on average. The enhanced efficiency makes this method effective for calculating the free energy of complex chemical reactions when the reaction coordinate can be unambiguously defined by a
Precession-driven flows in non-axisymmetric ellipsoids
Noir, Jerome
2014-01-01
We study the flow forced by precession in rigid non-axisymmetric ellipsoidal containers. To do so, we revisit the inviscid and viscous analytical models that have been previously developed for the spheroidal geometry by, respectively, Poincar\\'e (Bull. Astronomique, vol. XXVIII, 1910, pp. 1-36) and Busse (J. Fluid Mech., vol. 33, 1968, pp. 739-751), and we report the first numerical simulations of flows in such a geometry. In strong contrast with axisymmetric spheroids, where the forced flow is systematically stationary in the precessing frame, we show that the forced flow is unsteady and periodic. Comparisons of the numerical simulations with the proposed theoretical model show excellent agreement for both axisymmetric and non-axisymmetric containers. Finally, since the studied configuration corresponds to a tidally locked celestial body such as the Earth's Moon, we use our model to investigate the challenging but planetary-relevant limit of very small Ekman numbers and the particular case of our Moon.
A generic detailed rigid-body lumbar spine model
DEFF Research Database (Denmark)
De Zee, Mark; Hansen, Lone; Wong, Christian
2007-01-01
effort of different research groups. The model is defined in a text-based, declarative, object-oriented language in the AnyBody Modelling System software. Text-based models will facilitate sharing of the models between different research groups. The necessary data for the model has been taken from...... is relatively easy to share and modify due to the use of a well-defined and self-contained scripting language. Validation is though still necessary for specific cases....
Error in the description of foot kinematics due to violation of rigid body assumptions.
Nester, C J; Liu, A M; Ward, E; Howard, D; Cocheba, J; Derrick, T
2010-03-03
Kinematic data from rigid segment foot models inevitably includes errors because the bones within each segment move relative to each other. This study sought to define error in foot kinematic data due to violation of the rigid segment assumption. The research compared kinematic data from 17 different mid and forefoot rigid segment models to kinematic data of the individual bones comprising these segments. Kinematic data from a previous dynamic cadaver model study was used to derive individual bone as well as foot segment kinematics. Mean and maximum errors due to violation of the rigid body assumption varied greatly between models. The model with least error was the combination of navicular and cuboid (mean errors kinematics research study being undertaken.
A constrained generalised-α method for coupling rigid parallel chain kinematics and elastic bodies
Gransden, D.I.; Burkhard Bornemann, P.; Rose, M.; Nitzsche, F.
2015-01-01
A problem arises from combining flexible rotorcraft blades with stiffer mechanical links, which form a parallel kinematic chain. This paper introduces a method for solving index-3 differential algebraic equations for coupled stiff and elastic body systems with closed-loop kinematics. Rigid body dynamics and elastic body mechanics are independently described according to convenient mathematical measures. Holonomic constraint equations couple both the parallel chain kinematics and describe the ...
Energy Technology Data Exchange (ETDEWEB)
Ismail, Norilmi Amilia, E-mail: aenorilmi@usm.my [School of Aerospace Engineering, Engineering Campus, Universiti Sains Malaysia, 14300 Nibong Tebal, Pulau Pinang (Malaysia)
2016-02-01
The motorized momentum exchange tether (MMET) is capable of generating useful velocity increments through spin–orbit coupling. This study presents a comparative study of the velocity increments between the rigid body and flexible models of MMET. The equations of motions of both models in the time domain are transformed into a function of true anomaly. The equations of motion are integrated, and the responses in terms of the velocity increment of the rigid body and flexible models are compared and analysed. Results show that the initial conditions, eccentricity, and flexibility of the tether have significant effects on the velocity increments of the tether.
Control of fluid-containing rotating rigid bodies
Gurchenkov, Anatoly A
2013-01-01
This book is devoted to the study of the dynamics of rotating bodies with cavities containing liquid. Two basic classes of motions are analyzed: rotation and libration. Cases of complete and partial filling of cavities with ideal liquid and complete filling with viscous liquid are treated. The volume presents a method for obtaining relations between angular velocities perpendicular to main rotation and external force momentums, which are treated as control. The developed models and methods of solving dynamical problems as well as numerical methods for solving problems of optimal control can be
Numerical simulation of a moving rigid body in a rarefied gas
Shrestha, Samir; Tiwari, Sudarshan; Klar, Axel; Hardt, Steffen
2015-07-01
In this paper we present a numerical scheme to simulate a moving rigid body with arbitrary shape suspended in a rarefied gas. The rarefied gas is simulated by solving the Boltzmann equation using a DSMC particle method. The motion of the rigid body is governed by the Newton-Euler equations, where the force and the torque on the rigid body are computed from the momentum transfer of the gas molecules colliding with the body. On the other hand, the motion of the rigid body influences the gas flow in its surroundings. We validate the numerical scheme by considering a moving piston problem in 1D and the Einstein relation for Brownian motion of the suspended particle in 3D. In the piston problem it is shown that the equilibrium position of the moving piston converges to the analytical solution for a wide range of Knudsen numbers. In the case of Brownian motion the translational as well as the rotational degrees of freedom are taken into account. In this case it is shown that the numerically computed translational and rotational diffusion coefficients converge to the theoretical values. Finally, the motion of an object of complex shape under the influence of a thermophoretic force is investigated.
Explaining rigid dieting in normal-weight women: the key role of body image inflexibility.
Ferreira, Cláudia; Trindade, Inês A; Martinho, Ana
2016-03-01
Restrictive dieting is an increasing behavior presented by women in modern societies, independently of their weight. There are several known factors that motivate diet, namely a sense of dissatisfaction with one's body and unfavorable social comparisons based on physical appearance. However, dieting seems to have a paradoxical effect and has been considered a risk factor for weight gain and obesity in women and for maladaptive eating. Nevertheless, the study of the emotional regulation processes that explain the adoption of inflexible and rigid eating behaviors still remains little explored. In this line, the present study aims to explore why normal-weight women engage in highly rigid and inflexible diets. We hypothesize that body and weight dissatisfaction and unfavorable social comparisons based on physical appearance explain the adoption of inflexible eating rules, through the mechanisms of body image inflexibility. The current study comprised 508 normal-weight female college students. Path analyses were conducted to explore the study's hypotheses. Results revealed that the model explained 43 % of inflexible eating and revealed excellent fit indices. Furthermore, the unwillingness to experience unwanted events related to body image (body image inflexibility) mediated the impact of body dissatisfaction and unfavorable social comparisons on the adoption of inflexible eating rules. This study highlights the relevance of body image inflexibility to explain rigid eating attitudes, and it seems to be an important avenue for the development of interventions focusing on the promotion of adaptive attitudes towards body image and eating in young women.
Asymmetric steady streaming as a mechanism for acoustic propulsion of rigid bodies
Nadal, François; Lauga, Eric
2014-08-01
Recent experiments showed that standing acoustic waves could be exploited to induce self-propulsion of rigid metallic particles in the direction perpendicular to the acoustic wave. We propose in this paper a physical mechanism for these observations based on the interplay between inertial forces in the fluid and the geometrical asymmetry of the particle shape. We consider an axisymmetric rigid near-sphere oscillating in a quiescent fluid along a direction perpendicular to its symmetry axis. The kinematics of oscillations can be either prescribed or can result dynamically from the presence of an external oscillating velocity field. Steady streaming in the fluid, the inertial rectification of the time-periodic oscillating flow, generates steady stresses on the particle which, in general, do not average to zero, resulting in a finite propulsion speed along the axis of the symmetry of the particle and perpendicular to the oscillation direction. Our derivation of the propulsion speed is obtained at leading order in the Reynolds number and the deviation of the shape from that of a sphere. The results of our model are consistent with the experimental measurements, and more generally explains how time periodic forcing from an acoustic field can be harnessed to generate autonomous motion.
Compliant mechanism road bicycle brake: a rigid-body replacement case study
Energy Technology Data Exchange (ETDEWEB)
Olsen, Brian M [Los Alamos National Laboratory; Howell, Larry L [NON LANL; Magleby, Spencer P [NON LANL
2011-01-19
The design of high-performance bicycle brakes is complicated by the competing design objectives of increased performance and low weight. But this challenge also provides a good case study to demonstrate the design of compliant mechanisms to replace current rigid-link mechanisms. This paper briefly reviews current road brake designs, demonstrates the use of rigid-body replacement synthesis to design a compliant mechanism, and illustrates the combination of compliant mechanism design tools. The resulting concept was generated from the modified dual-pivot brake design and is a partially compliant mechanism where one pin has the dual role of a joint and a mounting pin. The pseudo-rigid-body model, finite element analysis, and optimization algorithms are used to generate design dimensions, and designs are considered for both titanium and E-glass flexures. The resulting design has the potential of reducing the part count and overall weight while maintaining a performance similar to the benchmark.
Reyhanoglu, Mahmut
1996-01-01
There has been much interest over the past decade in the problem of asymptotic stabilization of the angular velocity of a rigid body with only two torque inputs. The smooth feedback laws proposed in the literature provide asymptotic stability with nonexponential convergence rates. This paper propose
Reconstructing rotations and rigid body motions from exact point correspondences through reflections
Fontijne, D.; Dorst, L.; Dorst, L.; Lasenby, J.
2011-01-01
We describe a new algorithm to reconstruct a rigid body motion from point correspondences. The algorithm works by constructing a series of reflections which align the points with their correspondences one by one. This is naturally and efficiently implemented in the conformal model of geometric algeb
Rigid Body Time Integration by Convected Base Vectors with Implicit Constraints
DEFF Research Database (Denmark)
Krenk, Steen; Nielsen, Martin Bjerre
2013-01-01
of the kinetic energy used in the present formulation is deliberately chosen to correspond to a rigid body rotation, and the orthonormality constraints are introduced via the equivalent Green strain components of the base vectors. The particular form of the extended inertia tensor used here implies a set...
DEFF Research Database (Denmark)
Nielsen, Martin Bjerre; Krenk, Steen
2012-01-01
A conservative time integration algorithm for rigid body rotations is presented in a purely algebraic form in terms of the four quaternions components and the four conjugate momentum variables via Hamilton’s equations. The introduction of an extended mass matrix leads to a symmetric set of eight...
Euler-Poincaré Reduction of Externally Forced Rigid Body Motion
DEFF Research Database (Denmark)
Wisniewski, Rafal; Kulczycki, P.
2004-01-01
. Assuming that the system possesses symmetry and the configuration manifold corresponds to a Lie group, the Euler-Poincaré reduction breaks up the motion into separate equations of dynamics and kinematics. This becomes of particular interest for modelling, estimation and control of mechanical systems......-known Euler-Poincaré reduction to a rigid body motion with forcing....
Virtual fracture reduction of the acetabulum using a rigid body biomechanical model
Boudissa, Mehdi; Chabanas, Matthieu; Oliveri, Hadrien; Tonetti, Jérôme
2014-01-01
International audience; Acetabular fractures are a challenge in orthopaedic surgery. A simple rigid body biomechanical model of the hip is proposed to simulate the fracture reduction. The action of surgical tools can be simulated interactively, which enables clinicians to evaluate different strategies for a better surgical planning.
Lorentz Contraction, Bell's Spaceships and Rigid Body Motion in Special Relativity
Franklin, Jerrold
2010-01-01
The meaning of Lorentz contraction in special relativity and its connection with Bell's spaceships parable is discussed. The motion of Bell's spaceships is then compared with the accelerated motion of a rigid body. We have tried to write this in a simple form that could be used to correct students' misconceptions due to conflicting earlier…
Lorentz Contraction, Bell's Spaceships and Rigid Body Motion in Special Relativity
Franklin, Jerrold
2010-01-01
The meaning of Lorentz contraction in special relativity and its connection with Bell's spaceships parable is discussed. The motion of Bell's spaceships is then compared with the accelerated motion of a rigid body. We have tried to write this in a simple form that could be used to correct students' misconceptions due to conflicting earlier…
The Serret-Andoyer Formalism in Rigid-Body Dynamics: 1. Symmetries and Perturbations
2007-01-01
Aerospace Engineering, Technion–Israel Institute of Technology, Haifa, 32000 Israel 2 Grupo de Mecanica Espacial, Universidad de Zaragoza, Zaragoza, 50009...rigid-body dynamics and kinematics. Most popular is the set suggested in 1923 by Andoyer [20]. This set is not completely reduced: while three of its
A constrained generalised- method for coupling rigid parallel chain kinematics and elastic bodies
Gransden, Derek I.; Bornemann, P. Burkhard; Rose, Michael; Nitzsche, Fred
2015-03-01
A problem arises from combining flexible rotorcraft blades with stiffer mechanical links, which form a parallel kinematic chain. This paper introduces a method for solving index-3 differential algebraic equations for coupled stiff and elastic body systems with closed-loop kinematics. Rigid body dynamics and elastic body mechanics are independently described according to convenient mathematical measures. Holonomic constraint equations couple both the parallel chain kinematics and describe the coupling between the rigid and continuum bodies. Lagrange multipliers enforce the kinetic conditions for both sets of constraints. Additionally, to prevent numerical inaccuracy from inverting stiff mechanical matrices, a scaling factor normalises the dynamic tangential stiffness matrix. Finally, example tests show the verification of the algorithm with respect to existing computational tests and the accuracy of the model for cases relevant to the problem definition.
On the invariant motions of rigid body rotation over the fixed point, via Euler angles
Ershkov, Sergey V
2016-01-01
The generalized Euler case (rigid body rotation over the fixed point) is discussed here: - the center of masses of non-symmetric rigid body is assumed to be located at the equatorial plane on axis Oy which is perpendicular to the main principal axis Ox of inertia at the fixed point. Such a case was presented in the rotating coordinate system, in a frame of reference fixed in the rotating body for the case of rotation over the fixed point (at given initial conditions). In our derivation, we have represented the generalized Euler case in the fixed Cartesian coordinate system; so, the motivation of our ansatz is to elegantly transform the proper components of the previously presented solution from one (rotating) coordinate system to another (fixed) Cartesian coordinates. Besides, we have obtained an elegantly analytical case of general type of rotations; also, we have presented it in the fixed Cartesian coordinate system via Euler angles.
Institute of Scientific and Technical Information of China (English)
Yong Wang; Jian Kang
2015-01-01
In traditional inverse synthetic aperture radar (ISAR) imaging of moving targets with rotational parts, the micro-Doppler (m-D) effects caused by the rotational parts influence the quality of the radar images. Recently, L. Stankovic proposed an m-D removal method based on L-statistics, which has been proved effective and simple. The algorithm can extract the m-D effects according to different behaviors of signals induced by rotational parts and rigid bodies in time-frequency (T-F) domain. However, by removing m-D effects, some useful short time Fourier transform (STFT) samples of rigid bodies are also extracted, which induces the side lobe problem of rigid bodies. A parameter estimation method for rigid bodies after m-D removal is proposed, which can accurately re-cover rigid bodies and avoid the side lobe problem by only using m-D removal. Simulations are given to validate the effectiveness of the proposed method.
Pretorius, P Hendrik; Johnson, Karen L; King, Michael A
2016-06-01
We have recently been successful in the development and testing of rigid-body motion tracking, estimation and compensation for cardiac perfusion SPECT based on a visual tracking system (VTS). The goal of this study was to evaluate in patients the effectiveness of our rigid-body motion compensation strategy. Sixty-four patient volunteers were asked to remain motionless or execute some predefined body motion during an additional second stress perfusion acquisition. Acquisitions were performed using the standard clinical protocol with 64 projections acquired through 180 degrees. All data were reconstructed with an ordered-subsets expectation-maximization (OSEM) algorithm using 4 projections per subset and 5 iterations. All physical degradation factors were addressed (attenuation, scatter, and distance dependent resolution), while a 3-dimensional Gaussian rotator was used during reconstruction to correct for six-degree-of-freedom (6-DOF) rigid-body motion estimated by the VTS. Polar map quantification was employed to evaluate compensation techniques. In 54.7% of the uncorrected second stress studies there was a statistically significant difference in the polar maps, and in 45.3% this made a difference in the interpretation of segmental perfusion. Motion correction reduced the impact of motion such that with it 32.8 % of the polar maps were statistically significantly different, and in 14.1% this difference changed the interpretation of segmental perfusion. The improvement shown in polar map quantitation translated to visually improved uniformity of the SPECT slices.
Sevilla, A.; Martínez-Bazán, C.
2004-09-01
In the present work we study the large-scale helical vortex shedding regime in the wake of an axisymmetric body with a blunt trailing edge at high Reynolds numbers, both experimentally and by means of local, linear, and spatiotemporal stability analysis. In the instability analysis we take into account the detailed downstream evolution of the basic flow behind the body base. The study confirms the existence of a finite region of absolute instability for the first azimuthal number in the near field of the wake. Such instability is believed to trigger the large-scale helical vortex shedding downstream of the recirculating zone. Inhibition of vortex shedding is examined by blowing a given flow rate of fluid through the base of the slender body. The extent of the locally absolute region of the flow is calculated as a function of the bleed coefficient, Cb=qb/(πR2u∞), where qb is the bleed flow rate, R is the radius of the base, and u∞ is the incident free-stream velocity. It is shown that the basic flow becomes convectively unstable everywhere for a critical value of the bleed coefficient of Cb*˜0.13, such that no self-excited regime is expected for Cb>Cb*. In addition, we report experimental results of flow visualizations and hot-wire measurements for increasing values of the bleed coefficient. When a sufficient amount of base bleed is applied, flow visualizations indicate that vortex shedding is suppressed and that the mean flow becomes axisymmetric. The critical bleed coefficient predicted by linear instability analysis is shown to fall within the experimental values in the range of Reynolds numbers analyzed here.
Mutual potential between two rigid bodies with arbitrary shapes and mass distributions
Hou, Xiyun; Scheeres, Daniel J.; Xin, Xiaosheng
2016-09-01
Formulae to compute the mutual potential, force, and torque between two rigid bodies are given. These formulae are expressed in Cartesian coordinates using inertia integrals. They are valid for rigid bodies with arbitrary shapes and mass distributions. By using recursive relations, these formulae can be easily implemented on computers. Comparisons with previous studies show their superiority in computation speed. Using the algorithm as a tool, the planar problem of two ellipsoids is studied. Generally, potential truncated at the second order is good enough for a qualitative description of the mutual dynamics. However, for ellipsoids with very large non-spherical terms, higher order terms of the potential should be considered, at the cost of a higher computational cost. Explicit formulae of the potential truncated to the fourth order are given.
Conservative rigid body dynamics by convected base vectors with implicit constraints
DEFF Research Database (Denmark)
Krenk, Steen; Nielsen, Martin Bjerre
2014-01-01
A conservative time integration formulation is developed for rigid bodies based on a convected set of orthonormal base vectors. The base vectors are represented in terms of their absolute coordinates, and thus the formulation makes use of three translation components, plus nine components...... of the base vectors. Orthogonality and unit length of the base vectors are imposed by constraining the equivalent Green strain components, and the kinetic energy is represented corresponding to rigid body motion. The equations of motion are obtained via Hamilton’s equations including the zero......-strain conditions as well as external constraints via Lagrange multipliers. Subsequently, the Lagrange multipliers associated with the internal zero-strain constraints are eliminated by use of a set of orthogonality conditions between the generalized displacements and the momentum vector, leaving a set...
The tennis racket effect in a three-dimensional rigid body
Van Damme, L; Sugny, D
2016-01-01
We propose a complete theoretical description of the tennis racket effect, which occurs in the free rotation of a three-dimensional rigid body. This effect is characterized by a flip ($\\pi$- rotation) of the head of the racket when a full ($2\\pi$) rotation around the unstable inertia axis is considered. We describe the asymptotics of the phenomenon and conclude about the robustness of this effect with respect to the values of the moments of inertia and the initial conditions of the dynamics. This shows the generality of this geometric property which can be found in a variety of rigid bodies. A simple analytical formula is derived to estimate the twisting effect in the general case. Different examples are discussed.
The tennis racket effect in a three-dimensional rigid body
Van Damme, Léo; Mardešić, Pavao; Sugny, Dominique
2017-01-01
We propose a complete theoretical description of the tennis racket effect, which occurs in the free rotation of a three-dimensional rigid body. This effect is characterized by a flip (π- rotation) of the head of the racket when a full (2 π) rotation around the unstable inertia axis is considered. We describe the asymptotics of the phenomenon and conclude about the robustness of this effect with respect to the values of the moments of inertia and the initial conditions of the dynamics. This shows the generality of this geometric property which can be found in a variety of rigid bodies. A simple analytical formula is derived to estimate the twisting effect in the general case. Different examples are discussed.
THE DYNAMIC BUCKLING OF ELASTIC-PLASTIC COLUMN SUBJECTED TO AXIAL IMPACT BY A RIGID BODY
Institute of Scientific and Technical Information of China (English)
Han Zhijun; Wang Jingchao; Cheng Guoqiang; Ma Hongwei; Zhang Shanyuan
2005-01-01
The dynamic buckling of an elastic-plastic column subjected to axial impact by a rigid body has been discussed in this paper. The whole traveling process of elastic-plastic waves under impact action is analyzed with the characteristics method. The regularity of stress changes in both column ends and the first separating time of a rigid body and column are obtained. By using the energy principle and taking into account the propagation and reflection of stress waves the lateral disturbance equation is derived and the power series solution is given. In addition,the critical buckling condition can be obtained from the stability analysis of the solution. By numerical computation and analysis, the relationship among critical velocity and impact mass,hardening modulus, and buckling time is given.
Topological classification of the Goryachev integrable case in rigid body dynamics
Nikolaenko, S. S.
2016-01-01
A topological analysis of the Goryachev integrable case in rigid body dynamics is made on the basis of the Fomenko-Zieschang theory. The invariants (marked molecules) which are obtained give a complete description, from the standpoint of Liouville classification, of the systems of Goryachev type on various level sets of the energy. It turns out that on appropriate energy levels the Goryachev case is Liouville equivalent to many classical integrable systems and, in particular, the Joukowski, Clebsch, Sokolov and Kovalevskaya-Yehia cases in rigid body dynamics, as well as to some integrable billiards in plane domains bounded by confocal quadrics -- in other words, the foliations given by the closures of generic solutions of these systems have the same structure. Bibliography: 15 titles.
Respiratory motion correction in gated cardiac SPECT using quaternion-based, rigid-body registration
Parker, Jason G.; Mair, Bernard A.; Gilland, David R.
2009-01-01
In this article, a new method is introduced for estimating the motion of the heart due to respiration in gated cardiac SPECT using a rigid-body model with rotation parametrized by a unit quaternion. The method is based on minimizing the sum of squared errors between the reference and the deformed frames resulting from the usual optical flow constraint by using an optimized conjugate gradient routine. This method does not require any user-defined parameters or penalty terms, which simplifies i...
Conservative integration of rigid body motion by quaternion parameters with implicit constraints
DEFF Research Database (Denmark)
Nielsen, Martin Bjerre; Krenk, Steen
2012-01-01
An angular momentum and energy‐conserving time integration algorithm for rigid body rotation is formulated in terms of the quaternion parameters and the corresponding four‐component conjugate momentum vector via Hamilton's equations. The introduction of an extended mass matrix leads to a symmetri...... of momentum and energy. Implementation, conservation properties, and accuracy of the algorithm are illustrated by examples with a flying box and a spinning top. Copyright © 2012 John Wiley & Sons, Ltd....
Study of the kinematics of rigid body using the sliding vectors' theory
Llopis Cosin, Juan Vicente; Rubio Michavila, Constanza; Gasque Albalate, Maria; Quiles Casado, Susana De La Salud
2013-01-01
The sliding vector theory is a powerful tool for the study of the three parts of Classical Mechanics in vectorial formulation: Kinematics, Statics and Dynamics. Due to the great importance of the Vector Mechanics for their technical applications in engineering, this part of the Physics is studied in the first years of Engineering Degrees, as a fundamental topic included in the subjects of Physics. The rigid body model is the solid under study in Vectorial Mechanics. Firstly, in Ki...
Rigid-body kinematics versus flapping kinematics of a flapping wing micro air vehicle
Caetano, J.V.; Weehuizen, M.B.; De Visser, C.C.; De Croon, G.C.H.E.; de Mulder, M.
2015-01-01
Several formulations have been proposed to model the dynamics of ornithopters, with inconclusive results regarding the need for complex kinematic formulations. Furthermore, the impact of assumptions made in the collected results was never assessed by comparing simulations with real flight data. In this study two dynamic models of a Flapping Wing Micro Aerial Vehicle (FWMAV) were derived and compared: a) single rigid body aircraft equations of motion and b) Virtual Work Principle derivation fo...
Hamilton's Equations with Euler Parameters for Rigid Body Dynamics Modeling. Chapter 3
Shivarama, Ravishankar; Fahrenthold, Eric P.
2004-01-01
A combination of Euler parameter kinematics and Hamiltonian mechanics provides a rigid body dynamics model well suited for use in strongly nonlinear problems involving arbitrarily large rotations. The model is unconstrained, free of singularities, includes a general potential energy function and a minimum set of momentum variables, and takes an explicit state space form convenient for numerical implementation. The general formulation may be specialized to address particular applications, as illustrated in several three dimensional example problems.
Estimation of the ground shaking from the response of rigid bodies
Directory of Open Access Journals (Sweden)
Filomena de Silva
2016-12-01
Full Text Available The paper illustrates and compares simplified approaches to interpret the mechanisms of damage observed on rigid bodies in the cemetery of Amatrice, after the main shock (August 24, 2016, MW=6.0 of the Central Italy earthquake. The final goal of the work is to link the observed movements of the fallen objects to specific characteristics of the ground motion occurred at the specific site.
Eigenvalue analysis of a cantilever beam-rigid-body MEMS gyroscope
Lajimi, Seyed Amir Mousavi; Abdel-Rahman, Eihab
2014-01-01
The eigenvalues of a new microbeam-rigid-body gyroscope are computed and studied to show the variation of frequencies versus the input spin rate. To this end, assuming the harmonic solution of the dynamic equation of motion the characteristic equation is obtained and solved for the natural frequencies of the system in the rotating frame. It is shown that the difference between the natural frequencies (eigenvalues) proportionally grows with the input angular displacement rate.
Stability of the relative equilibria of a rigid body in a J2 gravity field
Wang, Yue; Xu, Shijie
2014-01-01
The motion of a point mass in the J2 problem is generalized to that of a rigid body in a J2 gravity field. Different with the original J2 problem, the gravitational orbit-rotation coupling of the rigid body is considered in this generalized problem. The linear stability of the classical type of relative equilibria of the rigid body, which have been obtained in our previous paper, is studied in the framework of geometric mechanics with the second-order gravitational potential. Non-canonical Hamiltonian structure of the problem, i.e., Poisson tensor, Casimir functions and equations of motion, are obtained through a Poisson reduction process by means of the symmetry of the problem. The linear system matrix at the relative equilibria is given through the multiplication of the Poisson tensor and Hessian matrix of the variational Lagrangian. Based on the characteristic equation of the linear system matrix, the conditions of linear stability of the relative equilibria are obtained. With the stability conditions obta...
On Classical Dynamics of Affinely-Rigid Bodies Subject to the Kirchhoff-Love Constraints
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Vasyl Kovalchuk
2010-04-01
Full Text Available In this article we consider the affinely-rigid body moving in the three-dimensional physical space and subject to the Kirchhoff-Love constraints, i.e., while it deforms homogeneously in the two-dimensional central plane of the body it simultaneously performs one-dimensional oscillations orthogonal to this central plane. For the polar decomposition we obtain the stationary ellipsoids as special solutions of the general, strongly nonlinear equations of motion. It is also shown that these solutions are conceptually different from those obtained earlier for the two-polar (singular value decomposition.
Analytic Theory and Control of the Motion of Spinning Rigid Bodies
Tsiotras, Panagiotis
1993-01-01
Numerical simulations are often resorted to, in order to understand the attitude response and control characteristics of a rigid body. However, this approach in performing sensitivity and/or error analyses may be prohibitively expensive and time consuming, especially when a large number of problem parameters are involved. Thus, there is an important role for analytical models in obtaining an understanding of the complex dynamical behavior. In this dissertation, new analytic solutions are derived for the complete attitude motion of spinning rigid bodies, under minimal assumptions. Hence, we obtain the most general solutions reported in the literature so far. Specifically, large external torques and large asymmetries are included in the problem statement. Moreover, problems involving large angular excursions are treated in detail. A new tractable formulation of the kinematics is introduced which proves to be extremely helpful in the search for analytic solutions of the attitude history of such kinds of problems. The main utility of the new formulation becomes apparent however, when searching for feedback control laws for stabilization and/or reorientation of spinning spacecraft. This is an inherently nonlinear problem, where standard linear control techniques fail. We derive a class of control laws for spin axis stabilization of symmetric spacecraft using only two pairs of gas jet actuators. Practically, this could correspond to a spacecraft operating in failure mode, for example. Theoretically, it is also an important control problem which, because of its difficulty, has received little, if any, attention in the literature. The proposed control laws are especially simple and elegant. A feedback control law that achieves arbitrary reorientation of the spacecraft is also derived, using ideas from invariant manifold theory. The significance of this research is twofold. First, it provides a deeper understanding of the fundamental behavior of rigid bodies subject to body
Meichsner, J
2015-01-01
Perturbations of satellite orbits in the gravitational field of a body with a mass monopole and arbitrary spin multipole moments are considered for an axisymmetric and stationary situation. Periodic and secular effects caused by the central gravitomagnetic field are derived by a first order perturbation theory. For a central spin-dipole field these results reduce to the well known Lense-Thirring effects.
Closed-Loop Control of Satellite Formations Using a Quasi-Rigid Body Formulation
Blake, Christopher; Misra, Arun K.
2011-04-01
Satellites in formation work together to fulfill the role of a larger satellite. The purpose of this article is to develop a quasi-rigid body formulation for modeling and controlling such a formation as a single entity. In this article, a definition of a quasi-rigid body coordinate frame is presented, which, when attached to a formation, conveniently describes its orientation in space. Using this formulation, the equations of motion for a satellite formation are recast, and natural circular formations are expressed more succinctly. When the J 2 perturbation is considered, a correction factor on the formation's spin rate is introduced. The control of a satellite formation can effectively be separated into (1) a control torque to maintain the attitude and (2) control forces that maintain the rigidity of the formation. With this in mind, a nonlinear Lyapunov controller is derived using the formulation, which acts on the formation as a whole. Simulations validate this controller and illustrate its utility for maintaining circular formations, in particular, in the presence of gravitational perturbations.
Dynamic analysis on generalized linear elastic body subjected to large scale rigid rotations
Institute of Scientific and Technical Information of China (English)
刘占芳; 颜世军; 符志
2013-01-01
The dynamic analysis of a generalized linear elastic body undergoing large rigid rotations is investigated. The generalized linear elastic body is described in kine-matics through translational and rotational deformations, and a modified constitutive relation for the rotational deformation is proposed between the couple stress and the curvature tensor. Thus, the balance equations of momentum and moment are used for the motion equations of the body. The floating frame of reference formulation is applied to the elastic body that conducts rotations about a fixed axis. The motion-deformation coupled model is developed in which three types of inertia forces along with their incre-ments are elucidated. The finite element governing equations for the dynamic analysis of the elastic body under large rotations are subsequently formulated with the aid of the constrained variational principle. A penalty parameter is introduced, and the rotational angles at element nodes are treated as independent variables to meet the requirement of C1 continuity. The elastic body is discretized through the isoparametric element with 8 nodes and 48 degrees-of-freedom. As an example with an application of the motion-deformation coupled model, the dynamic analysis on a rotating cantilever with two spatial layouts relative to the rotational axis is numerically implemented. Dynamic frequencies of the rotating cantilever are presented at prescribed constant spin velocities. The maximal rigid rotational velocity is extended for ensuring the applicability of the linear model. A complete set of dynamical response of the rotating cantilever in the case of spin-up maneuver is examined, it is shown that, under the ultimate rigid rotational velocities less than the maximal rigid rotational velocity, the stress strength may exceed the material strength tolerance even though the displacement and rotational angle responses are both convergent. The influence of the cantilever layouts on their responses and
Classical models of affinely-rigid bodies with "thickness" in degenerate dimension
Kovalchuk, Vasyl
2009-01-01
The special interest is devoted to such situations when the material space of our object with affine degrees of freedom has generally lower dimension than the one of the physical space. In other words when we have the $m$-dimensional affinely-rigid body moving in the $n$-dimensional physical space, $m
Rodriguez, G.
1988-01-01
The inverse and forward dynamics problems for a set of rigid bodies connected by hinges to form a topological tree are solved by using recursive techniques from linear filtering and smoothing theory. An inward filtering sequence computes a set of constraint moments and forces. This is followed by an outward sequence to determine a corresponding set of angular and linear accelerations. An inward sequence begins at the tips of all of the terminal bodies of the tree and proceeds inwardly through all of the branches until it reaches the root. Similarly, an outward sequence begins at the root and propagates to all of the tree branches until it reaches the tips of the terminal bodies. The paper also provides an approach to evaluate recursively the composite multibody system inertia matrix and its inverse.
Implementation of Kane's Method for a Spacecraft Composed of Multiple Rigid Bodies
Stoneking, Eric T.
2013-01-01
Equations of motion are derived for a general spacecraft composed of rigid bodies connected via rotary (spherical or gimballed) joints in a tree topology. Several supporting concepts are developed in depth. Basis dyads aid in the transition from basis-free vector equations to component-wise equations. Joint partials allow abstraction of 1-DOF, 2-DOF, 3-DOF gimballed and spherical rotational joints to a common notation. The basic building block consisting of an "inner" body and an "outer" body connected by a joint enables efficient organization of arbitrary tree structures. Kane's equation is recast in a form which facilitates systematic assembly of large systems of equations, and exposes a relationship of Kane's equation to Newton and Euler's equations which is obscured by the usual presentation. The resulting system of dynamic equations is of minimum dimension, and is suitable for numerical solution by computer. Implementation is ·discussed, and illustrative simulation results are presented.
A refined technique to calculate finite helical axes from rigid body trackers.
McLachlin, Stewart D; Ferreira, Louis M; Dunning, Cynthia E
2014-12-01
Finite helical axes (FHAs) are a potentially effective tool for joint kinematic analysis. Unfortunately, no straightforward guidelines exist for calculating accurate FHAs using prepackaged six degree-of-freedom (6 DOF) rigid body trackers. Thus, this study aimed to: (1) describe a protocol for calculating FHA parameters from 6 DOF rigid body trackers using the screw matrix and (2) to maximize the number of accurate FHAs generated from a given data set using a moving window analysis. Four Optotrak® Smart Markers were used as the rigid body trackers, two moving and two fixed, at different distances from the hinge joint of a custom-machined jig. 6D OF pose information was generated from 51 static positions of the jig rotated and fixed in 0.5 deg increments up to 25 deg. Output metrics included the FHA direction cosines, the rotation about the FHA, the translation along the axis, and the intercept of the FHA with the plane normal to the jig's hinge joint. FHA metrics were calculated using the relative tracker rotation from the starting position, and using a moving window analysis to define a minimum acceptable rotational displacement between the moving tracker data points. Data analysis found all FHA rotations calculated from the starting position were within 0.15 deg of the prescribed jig rotation. FHA intercepts were most stable when determined using trackers closest to the hinge axis. Increasing the moving window size improved the FHA direction cosines and center of rotation accuracy. Window sizes larger than 2 deg had an intercept deviation of less than 1 mm. Furthermore, compared to the 0 deg window size, the 2 deg window had a 90% improvement in FHA intercept precision while generating almost an equivalent number of FHA axes. This work identified a solution to improve FHA calculations for biomechanical researchers looking to describe changes in 3D joint motion.
Simulating Dynamics of the System of Articulated Rigid Bodies with Joint Friction
Directory of Open Access Journals (Sweden)
M. V. Michaylyuk
2016-01-01
Full Text Available The subject of the work is to simulate dynamics of the system of articulated rigid bodies in the virtual environment complexes. The work aim is to develop algorithms and methods to simulate the multi-body system dynamics with joint friction to ensure all calculations in real time in line with visual realistic behavior of objects in a scene.The paper describes the multibody system based on a maximal set of coordinates, and to simulate the joint friction is used a Coulomb's law of dry friction. Joints are described using the holonomic constraints and their derivatives that specify the constraints on velocities of joined bodies. Based on The Coulomb’s law a correlation for the friction impulse values has been derived as an inequality. If the friction impulse performs a constraint that is a lack of relative motion of two joint-joined bodies, there is a static friction in the joint. Otherwise, there is a dynamic friction in the joint. Using a semi-implicit Euler method allows us to describe dynamics of articulated rigid bodies with joint friction as a system of linear algebraic equations and inequalities for the unknown velocities and impulse values.To solve the obtained system of equations and inequalities is used an iterative method of sequential impulses, which sequentially processes constraints for each joint with impulse calculation and its application to the joined bodies rather than considers the entire system. To improve the method convergence, at each iteration the calculated impulses are accumulated for their further using as an initial approximation at the next step of simulation.The proposed algorithms and methods have been implemented in the training complex dynamics subsystem, developed in SRISA RAS. Evaluation of these methods and algorithms has demonstrated their full adequacy to requirements for virtual environment systems and training complexes.
Fast time-reversible algorithms for molecular dynamics of rigid-body systems
Kajima, Yasuhiro; Hiyama, Miyabi; Ogata, Shuji; Kobayashi, Ryo; Tamura, Tomoyuki
2012-06-01
In this paper, we present time-reversible simulation algorithms for rigid bodies in the quaternion representation. By advancing a time-reversible algorithm [Y. Kajima, M. Hiyama, S. Ogata, and T. Tamura, J. Phys. Soc. Jpn. 80, 114002 (2011), 10.1143/JPSJ.80.114002] that requires iterations in calculating the angular velocity at each time step, we propose two kinds of iteration-free fast time-reversible algorithms. They are easily implemented in codes. The codes are compared with that of existing algorithms through demonstrative simulation of a nanometer-sized water droplet to find their stability of the total energy and computation speeds.
An implicit time-stepping scheme for rigid body dynamics with Coulomb friction
Energy Technology Data Exchange (ETDEWEB)
STEWART,DAVID; TRINKLE,JEFFREY C.
2000-02-15
In this paper a new time-stepping method for simulating systems of rigid bodies is given. Unlike methods which take an instantaneous point of view, the method is based on impulse-momentum equations, and so does not need to explicitly resolve impulsive forces. On the other hand, the method is distinct from previous impulsive methods in that it does not require explicit collision checking and it can handle simultaneous impacts. Numerical results are given for one planar and one three-dimensional example, which demonstrate the practicality of the method, and its convergence as the step size becomes small.
Comparison of Point and Line Features and Their Combination for Rigid Body Motion Estimation
DEFF Research Database (Denmark)
Pilz, Florian; Pugeault, Nicolas; Krüger, Norbert
2009-01-01
This paper discusses the usage of dierent image features and their combination in the context of estimating the motion of rigid bodies (RBM estimation). From stereo image sequences, we extract line features at local edges (coded in so called multi-modal primitives) as well as point features (by...... evaluate and compare the results using line and point features as 3D-2D constraints and we discuss the qualitative advantages and disadvantages of both feature types for RBM estimation. We also demonstrate an improvement in robustness through the combination of these features on large data sets...
DEFF Research Database (Denmark)
Nielsen, Martin Bjerre; Krenk, Steen
2012-01-01
A conservative time integration algorithm for rigid body rotations is presented in a purely algebraic form in terms of the four quaternions components and the four conjugate momentum variables via Hamilton’s equations. The introduction of an extended mass matrix leads to a symmetric set of eight...... state-space equations where constraints are embedded without explicit use of Lagrange multipliers. The algorithm is developed by forming a finite increment of the Hamiltonian, which defines the proper selection of increments and mean values that leads to conservation of energy and momentum. The accuracy...... and conservation properties are illustrated by examples....
Rotational kinematics of a rigid body about a fixed axis: development and analysis of an inventory
Mashood, K. K.; Singh, Vijay A.
2015-07-01
We present the development, administration, and analysis of a focused inventory on the rotational kinematics of a rigid body around a fixed axis. The inventory, which is made up of 13 multiple-choice questions, was developed on the basis of interactions with students and teachers. The systematic and iterative aspects of the construction of the inventory are illustrated. The questions, which were validated, were administered to a set of teachers (N = 25) and two groups of preuniversity students (N = 74 and 905) in India. Students, as well as teachers, exhibited difficulties in applying the operational definition of angular velocity to a rigid body. Many erroneously assumed that an angular acceleration cannot exist without a net torque. Patterns of reasoning resulting in errors were identified and categorized under four broad themes. These include inappropriate extensions of familiar procedural practices, reasoning cued by primitive elements in thought, lack of differentiation between related but distinct concepts, and indiscriminate use of equations. The inventory was also administered to introductory-level students (N = 384) at the University of Washington. Popular distractors to most items were similar to the Indian students.
Simulation of extension, radial and ulnar deviation of the wrist with a rigid body spring model.
Fischli, S; Sellens, R W; Beek, M; Pichora, D R
2009-06-19
A novel computational model of the wrist that predicts carpal bone motion was developed in order to investigate the complex kinematics of the human wrist. This rigid body spring model (RBSM) of the wrist was built using surface models of the eight carpal bones, the bases of the five metacarpal bones, and the distal parts of the ulna and radius, all obtained from computed tomography (CT) scans of a cadaver upper limb. Elastic contact conditions between the rigid bodies modeled the influence of the cartilage layers, and ligamentous structures were constructed using nonlinear, tension-only spring elements. Motion of the wrist was simulated by applying forces to the tendons of the five main wrist muscles modeled. Three wrist motions were simulated: extension, ulnar deviation and radial deviation. The model was tested and tuned by comparing the simulated displacement and orientation of the carpal bones with previously obtained CT-scans of the same cadaver arm in deviated (45 degrees ulnar and 15 degrees radial), and extended (57 degrees ) wrist positions. Simulation results for the scaphoid, lunate, capitate, hamate and triquetrum are presented here and provide credible prediction of carpal bone movement. These are the first reported results of such a model. They indicate promise that this model will assist in future wrist kinematics investigations. However, further optimization and validation are required to define and guarantee the validity of results.
The general problem of the motion of coupled rigid bodies about a fixed point
Leimanis, Eugene
1965-01-01
In the theory of motion of several coupled rigid bodies about a fixed point one can distinguish three basic ramifications. 1. The first, the so-called classical direction of investigations, is concerned with particular cases of integrability ot the equations of motion of a single rigid body about a fixed point,1 and with their geo metrical interpretation. This path of thought was predominant until the beginning of the 20th century and its most illustrious represen tatives are L. EULER (1707-1783), J L. LAGRANGE (1736-1813), L. POINSOT (1777-1859), S. V. KOVALEVSKAYA (1850-1891), and others. Chapter I of the present monograph intends to reflect this branch of investigations. For collateral reading on the general questions dealt with in this chapter the reader is referred to the following textbooks and reports: A. DOMOGAROV [1J, F. KLEIN and A. SOMMERFELD [11, 1 , 1 J, A. G. 2 3 GREENHILL [10J, A. GRAY [1J, R. GRAMMEL [4 J, E. J. ROUTH [21' 2 , 1 2 31' 32J, J. B. SCARBOROUGH [1J, and V. V. GOLUBEV [1, 2J.
The generalized Euler-Poinsot rigid body equations: explicit elliptic solutions
Fedorov, Yuri N.; Maciejewski, Andrzej J.; Przybylska, Maria
2013-10-01
The classical Euler-Poinsot case of the rigid body dynamics admits a class of simple but non-trivial integrable generalizations, which modify the Poisson equations describing the motion of the body in space. These generalizations possess first integrals which are polynomial in the angular momenta. We consider the modified Poisson equations as a system of linear equations with elliptic coefficients and show that all the solutions of it are single-valued. By using the vector generalization of the Picard theorem, we derive the solutions explicitly in terms of sigma-functions of the corresponding elliptic curve. The solutions are accompanied by a numerical example. We also compare the generalized Poisson equations with the classical third order Halphen equation.
Quantifying Rigid and Nonrigid Motion of Liver Tumors During Stereotactic Body Radiation Therapy
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Xu, Qianyi, E-mail: xuqianyi@gmail.com [Department of Radiation Oncology, MD Anderson Cancer Center at Cooper, Camden, New Jersey (United States); Hanna, George [Department of Radiation Oncology, MD Anderson Cancer Center at Cooper, Camden, New Jersey (United States); Grimm, Jimm [Department of Radiation Oncology, Holy Redeemer Hospital, Bott Cancer Center, Meadowbrook, Pennsylvania (United States); Kubicek, Gregory [Department of Radiation Oncology, MD Anderson Cancer Center at Cooper, Camden, New Jersey (United States); Pahlajani, Niraj [Department of Radiation Oncology, First Radiation and Oncology Group, Jacksonville, Florida (United States); Asbell, Sucha [Department of Radiation Oncology, MD Anderson Cancer Center at Cooper, Camden, New Jersey (United States); Fan, Jiajin [Department of Radiation Oncology, Fox Chase Cancer Center, Philadelphia, Pennsylvania (United States); Chen, Yan; LaCouture, Tamara [Department of Radiation Oncology, MD Anderson Cancer Center at Cooper, Camden, New Jersey (United States)
2014-09-01
Purpose: To quantify rigid and nonrigid motion of liver tumors using reconstructed 3-dimensional (3D) fiducials from stereo imaging during CyberKnife-based stereotactic body radiation therapy (SBRT). Methods and Materials: Twenty-three liver patients treated with 3 fractions of SBRT were used in this study. After 2 orthogonal kilovoltage images were taken during treatment, the 3D locations of the fiducials were generated by the CyberKnife system and validated using geometric derivations. A total of 4824 pairs of kilovoltage images from start to end of treatment were analyzed. For rigid motion, the rotational angles and translational shifts were reported by aligning 3D fiducial groups from different image pairs, using least-squares fitting. For nonrigid motion, we quantified interfractional tumor volume variations by using the proportional volume derived from the fiducials, which correlates to the sum of interfiducial distances. The individual fiducial displacements were also reported (1) after rigid corrections and (2) without angle corrections. Results: The proportional volume derived by the fiducials demonstrated a volume-increasing trend in the second (101.9% ± 3.6%) and third (101.0 ± 5.9%) fractions among most patients, possibly due to radiation-induced edema. For all patients, the translational shifts in left-right, anteroposterior, and superoinferior directions were 2.1 ± 2.3 mm, 2.9 ± 2.8 mm, and 6.4 ± 5.5 mm, respectively. The greatest translational shifts occurred in the superoinferior direction, likely due to respiratory motion from the diaphragm. The rotational angles in roll, pitch, and yaw were 1.2° ± 1.8°, 1.8° ± 2.4°, and 1.7° ± 2.1°, respectively. The 3D individual fiducial displacements with rigid corrections were 0.2 ± 0.2 mm and increased to 0.5 ± 0.4 mm without rotational corrections. Conclusions: Accurate 3D locations of internal fiducials can be reconstructed from stereo imaging during treatment. As an
Chi, Heng; Lopez-Pamies, Oscar; Paulino, Glaucio H.
2016-02-01
This paper presents a new variational principle in finite elastostatics applicable to arbitrary elastic solids that may contain constitutively rigid spatial domains (e.g., rigid inclusions). The basic idea consists in describing the constitutive rigid behavior of a given spatial domain as a set of kinematic constraints over the boundary of the domain. From a computational perspective, the proposed formulation is shown to reduce to a set of algebraic constraints that can be implemented efficiently in terms of both single-field and mixed finite elements of arbitrary order. For demonstration purposes, applications of the proposed rigid-body-constraint formulation are illustrated within the context of elastomers, reinforced with periodic and random distributions of rigid filler particles, undergoing finite deformations.
Directory of Open Access Journals (Sweden)
G. Paterakis
2013-01-01
Full Text Available The work presents comparisons of the flame stabilization characteristics of axisymmetric disk and 2D slender bluff-body burner configurations, operating with inlet mixture stratification, under ultralean conditions. A double cavity propane air premixer formed along three concentric disks, supplied with a radial equivalence ratio gradient the afterbody disk recirculation, where the first flame configuration is stabilized. Planar fuel injection along the center plane of the leading face of a slender square cylinder against the approach cross-flow results in a stratified flame configuration stabilized alongside the wake formation region in the second setup. Measurements of velocities, temperatures, OH∗ and CH∗ chemiluminescence, local extinction criteria, and large-eddy simulations are employed to examine a range of ultralean and close to extinction flame conditions. The variations of the reacting front disposition within these diverse reacting wake topologies, the effect of the successive suppression of heat release on the near flame region characteristics, and the reemergence of large-scale vortical activity on approach to lean blowoff (LBO are investigated. The cross-correlation of the performance of these two popular flame holders that are at the opposite ends of current applications might offer helpful insights into more effective control measures for expanding the operational margin of a wider range of stabilization configurations.
Worst-case analysis of target localization errors in fiducial-based rigid body registration
Shamir, Reuben R.; Joskowicz, Leo
2009-02-01
Fiducial-based rigid registration is the preferred method for aligning the preoperative image with the intra-operative physical anatomy in existing image-guided surgery systems. After registration, the targets locations usually cannot be measured directly, so the Target Registration Error (TRE) is often estimated with the Fiducial Registration Error (FRE), or with Fitzpatrick TRE (FTRE) estimation formula. However, large discrepancies between the FRE and the TRE have been exemplified in hypothetical setups and have been observed in the clinic. In this paper, we formally prove that in the worst case the FRE and the TRE, and the FTRE and the TRE are independent, regardless of the target location, it location, the number of fiducials, and their configuration. The worst case occurs when the unknown Fiducial Localization Error (FLE) is modeled as an affine anisotropic inhomogeneous bias. Our results generalize previous examples, contribute to the mathematical understanding of TRE estimation in fiducial-based rigid-body registration, and strengthen the need for realistic and reliable FLE models and effective TRE estimation methods.
Constrained non-rigid registration for whole body image registration: method and validation
Li, Xia; Yankeelov, Thomas E.; Peterson, Todd E.; Gore, John C.; Dawant, Benoit M.
2007-03-01
3D intra- and inter-subject registration of image volumes is important for tasks that include measurements and quantification of temporal/longitudinal changes, atlas-based segmentation, deriving population averages, or voxel and tensor-based morphometry. A number of methods have been proposed to tackle this problem but few of them have focused on the problem of registering whole body image volumes acquired either from humans or small animals. These image volumes typically contain a large number of articulated structures, which makes registration more difficult than the registration of head images, to which the vast majority of registration algorithms have been applied. To solve this problem, we have previously proposed an approach, which initializes an intensity-based non-rigid registration algorithm with a point based registration technique [1, 2]. In this paper, we introduce new constraints into our non-rigid registration algorithm to prevent the bones from being deformed inaccurately. Results we have obtained show that the new constrained algorithm leads to better registration results than the previous one.
Quantitative Validation of a Human Body Finite Element Model Using Rigid Body Impacts.
Vavalle, Nicholas A; Davis, Matthew L; Stitzel, Joel D; Gayzik, F Scott
2015-09-01
Validation is a critical step in finite element model (FEM) development. This study focuses on the validation of the Global Human Body Models Consortium full body average male occupant FEM in five localized loading regimes-a chest impact, a shoulder impact, a thoracoabdominal impact, an abdominal impact, and a pelvic impact. Force and deflection outputs from the model were compared to experimental traces and corridors scaled to the 50th percentile male. Predicted fractures and injury severity measures were compared to evaluate the model's injury prediction capabilities. The methods of ISO/TS 18571 were used to quantitatively assess the fit of model outputs to experimental force and deflection traces. The model produced peak chest, shoulder, thoracoabdominal, abdominal, and pelvis forces of 4.8, 3.3, 4.5, 5.1, and 13.0 kN compared to 4.3, 3.2, 4.0, 4.0, and 10.3 kN in the experiments, respectively. The model predicted rib and pelvic fractures related to Abbreviated Injury Scale scores within the ranges found experimentally all cases except the abdominal impact. ISO/TS 18571 scores for the impacts studied had a mean score of 0.73 with a range of 0.57-0.83. Well-validated FEMs are important tools used by engineers in advancing occupant safety.
On the rotational equations of motion in rigid body dynamics when using Euler parameters.
Sherif, Karim; Nachbagauer, Karin; Steiner, Wolfgang
Many models of three-dimensional rigid body dynamics employ Euler parameters as rotational coordinates. Since the four Euler parameters are not independent, one has to consider the quaternion constraint in the equations of motion. This is usually done by the Lagrange multiplier technique. In the present paper, various forms of the rotational equations of motion will be derived, and it will be shown that they can be transformed into each other. Special attention is hereby given to the value of the Lagrange multiplier and the complexity of terms representing the inertia forces. Particular attention is also paid to the rotational generalized external force vector, which is not unique when using Euler parameters as rotational coordinates.
Mazur, Alexey K.
1999-07-01
Internal coordinate molecular dynamics (ICMD) is a recent efficient method for modeling polymer molecules which treats them as chains of rigid bodies rather than ensembles of point particles as in Cartesian MD. Unfortunately, it is readily applicable only to linear or tree topologies without closed flexible loops. Important examples violating this condition are sugar rings of nucleic acids, proline residues in proteins, and also disulfide bridges. This paper presents the first complete numerical solution of the chain closure problem within the context of ICMD. The method combines natural implicit fixation of bond lengths and bond angles by the choice of internal coordinates with explicit constraints similar to Cartesian dynamics used to maintain the chain closure. It is affordable for large molecules and makes possible 3-5 times faster dynamics simulations of molecular systems with flexible rings, including important biological objects like nucleic acids and disulfide-bonded proteins.
Dynamics on strata of trigonal Jacobians and some integrable problems of rigid body motion
Braden, H. W.; Enolski, V. Z.; Fedorov, Yu N.
2013-07-01
We present an algebraic geometrical and analytical description of the Goryachev case of rigid body motion. It belongs to a family of systems sharing the same properties: although completely integrable, they are not algebraically integrable, their solution is not meromorphic in the complex time and involves dynamics on the strata of the Jacobian varieties of trigonal curves. Although the strata of hyperelliptic Jacobians have already appeared in the literature in the context of some dynamical systems, the Goryachev case is the first example of an integrable system whose solution involves a more general curve. Several new features (and formulae) are encountered in the solution given in terms of sigma-functions of such a curve.
DEFF Research Database (Denmark)
Sönmez, Ümit; Tutum, Cem Celal
2008-01-01
In this work, a new compliant bistable mechanism design is introduced. The combined use of pseudo-rigid-body model (PRBM) and the Elastica buckling theory is presented for the first time to analyze the new design. This mechanism consists of the large deflecting straight beams, buckling beams......, and a slider. The kinematic analysis of this new mechanism is studied, using nonlinear Elastica buckling beam theory, the PRBM of a large deflecting cantilever beam, the vector loop closure equations, and numerically solving nonlinear algebraic equations. A design method of the bistable mechanism...... and the buckling Elastica solution for an original compliant mechanism kinematic analysis. New compliant mechanism designs are presented to highlight where such combined kinematic analysis is required....
DYNAMIC BUCKLING OF ELASTIC-PLASTIC COLUMN IMPACTED BY RIGID BODY
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The dynamic buckling of an elastic-plastic column subjected to an axial impact by a rigid body was discussed by using the energy law. The traveling process of elastic-plastic waves under impact action was analyzed by characteristics method. The equation of lateral disturbance used to analyze the problem was developed by taking into account the effect of elastic-plastic stress wave. The power series solution of this problem has been the power series approach. The buckling criterion of this problem was proposed by analyzing the characteristics of the solution. The relationship among critical velocity and impact mass, critical buckling length, hardening modulus was given by using theoretical analysis and numerical computation.
On docking, scoring and assessing protein-DNA complexes in a rigid-body framework.
Directory of Open Access Journals (Sweden)
Marc Parisien
Full Text Available We consider the identification of interacting protein-nucleic acid partners using the rigid body docking method FTdock, which is systematic and exhaustive in the exploration of docking conformations. The accuracy of rigid body docking methods is tested using known protein-DNA complexes for which the docked and undocked structures are both available. Additional tests with large decoy sets probe the efficacy of two published statistically derived scoring functions that contain a huge number of parameters. In contrast, we demonstrate that state-of-the-art machine learning techniques can enormously reduce the number of parameters required, thereby identifying the relevant docking features using a miniscule fraction of the number of parameters in the prior works. The present machine learning study considers a 300 dimensional vector (dependent on only 15 parameters, termed the Chemical Context Profile (CCP, where each dimension reflects a specific type of protein amino acid-nucleic acid base interaction. The CCP is designed to capture the chemical complementarities of the interface and is well suited for machine learning techniques. Our objective function is the Chemical Context Discrepancy (CCD, which is defined as the angle between the native system's CCP vector and the decoy's vector and which serves as a substitute for the more commonly used root mean squared deviation (RMSD. We demonstrate that the CCP provides a useful scoring function when certain dimensions are properly weighted. Finally, we explore how the amino acids on a protein's surface can help guide DNA binding, first through long-range interactions, followed by direct contacts, according to specific preferences for either the major or minor grooves of the DNA.
The Effect of Water Compressibility on a Rigid Body Movement in Two Phase Flow
Park, Chan Wook; Kim, Hak Sun; Lee, Sungsu
2008-11-01
The motion of a rigid body in a tube full of water-filled, initiated by a sudden release of highly pressurized air is simulated presuming the flow field as a two dimensional one. The effects of water compressibility on the body movement are investigated, comparing results based on the Fluent VOF model where water is treated as an incompressible medium with those from the presently developed VOF scheme. The present model considers compressibility of both air and water. The Fluent results show that the body moves farther and at higher speeds than the present ones. As time proceeds, the relative difference of speed and displacement between the two results drops substantially, after acoustic waves in water traverse and return the full length of the tube several times. To estimate instantaneous accelerations, however, requires implementation of the water compressibility effect as discrepancies between them do not decrease even after several pressure wave cycles. This work was supported by a research fund granted from Agency for Defense Development, South Korea.
Kia, T.; Longuski, J. M.
1984-01-01
Analytic error bounds are presented for the solutions of approximate models for self-excited near-symmetric rigid bodies. The error bounds are developed for analytic solutions to Euler's equations of motion. The results are applied to obtain a simplified analytic solution for Eulerian rates and angles. The results of a sample application of the range and error bound expressions for the case of the Galileo spacecraft experiencing transverse torques demonstrate the use of the bounds in analyses of rigid body spin change maneuvers.
DEFF Research Database (Denmark)
de Vaal, Jacobus B.; Hansen, Martin Otto Laver; Moan, Torgeir
2014-01-01
This paper discusses the influence of rigid body motions on rotor induced velocities and aerodynamic loads of a floating horizontal axis wind turbine. Analyses are performed with a simplified free wake vortex model specifically aimed at capturing the unsteady and non-uniform inflow typically...... experienced by a floating wind turbine. After discussing the simplified model in detail, comparisons are made to a state of the art free wake vortex code, using test cases with prescribed platform motion. It is found that the simplified model compares favourably with a more advanced numerical model......, and captures the essential influences of rigid body motions on the rotor loads, induced velocities and wake influence....
Amel'kin, N. I.
2010-01-01
Steady motions of a rigid body with a control momentum gyroscope are studied versus the gimbal axis direction relative to the body and the magnitude of the system angular momentum. The study is based on a formula that gives a parametric representation of the set of the system steady motions in terms
Motion of a rigid body in a tidal field an application to elliptical galaxies in clusters
Ciotti, L
1998-01-01
We investigate the motion, near the equilibrium configurations, of an initially spinless rigid body subject to an external tidal field. Two cases are considered: when the center of mass of the body is at rest at the equilibrium point of the field generated by a generic mass distribution, and when it is placed on a circular orbit subject to a spherically symmetric potential. A complete analysis of the equilibrium configurations is carried out for both cases. First, we derive the conditions for the stable equilibria, and then we analyze the frequencies of oscillations around the equilibrium positions. In view of these results, we consider the problem of alignment of galaxies in clusters. After estimating the period of the oscillations induced on the galaxies by the tidal field of the cluster, we discuss the possible effect of resonances between stellar orbits inside the galaxy and the oscillations of the galaxy as a whole; this may be a mechanism responsible for producing an intracluster stellar population.
iCub Whole-body Control through Force Regulation on Rigid Noncoplanar Contacts
Directory of Open Access Journals (Sweden)
Francesco eNori
2015-03-01
Full Text Available This paper details the implementation on the humanoid robot iCub of state-of-the-art algorithms for whole-body control. We regulate the forces between the robot and its surrounding environment to stabilize a desired robot posture. We assume that the forces and torques are exerted on rigid contacts. The validity of this assumption is guaranteed by constraining the contact forces and torques, e.g. the contact forces must belong to the associated friction cones. The implementation of this control strategy requires to estimate the external forces acting on the robot, and the internal joint torques. We then detail algorithms to obtain these estimations when using a robot with an iCub-like sensor set, i.e. distributed six-axis force-torque sensors and whole-body tactile sensors. A general theory for identifying the robot inertial parameters is also presented. From an actuation standpoint, we show how to implement a joint torque control in the case of DC brushless motors. In addition, the coupling mechanism of the iCub torso is investigated. The soundness of the entire control architecture is validated in a real scenario involving the robot iCub balancing and making contacts at both arms.
Directory of Open Access Journals (Sweden)
Reza Afghani
2016-06-01
Full Text Available Herein, we present the case of a 45-years-old woman with a foreign body (dental prosthesis ingestion lodged in the esophagus(Figure.1. The foreign body was extracted by rigid esophagoscopy after severe manipulation. In 24 hours, the patient became febrile with emphysema in the neck. laboratory data showed leukocytosis and CT scan revealed signs of esophageal perforation(Figure.2. Surgical exploration and drainage of the neck and mediastinum performed through a collar incision in the neck extended to the anterior of SCM in both sides, but we didn't perform feeding jejunostomy. We inserted one corrugated drain in every side of the neck(Figure.3.Patient was NPO for two weeks and brief total parenteral nutrition (TPN provided her calory.Finally,we succeeded to fistulized the perforation to the skin and control the mediastinitis(Figure.4.Patient regained oral feeding gradually after two weeks NPO. The follow-up esophagogram revealed the passage of the contrast to the distal esophagus with no leak and fistula.Early recognition of perforation could interrupt major operation to control catastrophic complication.
Borazjani, Iman; Ge, Liang; Sotiropoulos, Fotis
2008-08-10
The sharp-interface CURVIB approach of Ge and Sotiropoulos [L. Ge, F. Sotiropoulos, A Numerical Method for Solving the 3D Unsteady Incompressible Navier-Stokes Equations in Curvilinear Domains with Complex Immersed Boundaries, Journal of Computational Physics 225 (2007) 1782-1809] is extended to simulate fluid structure interaction (FSI) problems involving complex 3D rigid bodies undergoing large structural displacements. The FSI solver adopts the partitioned FSI solution approach and both loose and strong coupling strategies are implemented. The interfaces between immersed bodies and the fluid are discretized with a Lagrangian grid and tracked with an explicit front-tracking approach. An efficient ray-tracing algorithm is developed to quickly identify the relationship between the background grid and the moving bodies. Numerical experiments are carried out for two FSI problems: vortex induced vibration of elastically mounted cylinders and flow through a bileaflet mechanical heart valve at physiologic conditions. For both cases the computed results are in excellent agreement with benchmark simulations and experimental measurements. The numerical experiments suggest that both the properties of the structure (mass, geometry) and the local flow conditions can play an important role in determining the stability of the FSI algorithm. Under certain conditions unconditionally unstable iteration schemes result even when strong coupling FSI is employed. For such cases, however, combining the strong-coupling iteration with under-relaxation in conjunction with the Aitken's acceleration technique is shown to effectively resolve the stability problems. A theoretical analysis is presented to explain the findings of the numerical experiments. It is shown that the ratio of the added mass to the mass of the structure as well as the sign of the local time rate of change of the force or moment imparted on the structure by the fluid determine the stability and convergence of the FSI
Fitzpatrick, P. M.; Harmon, G. R.; Liu, J. J. F.; Cochran, J. E.
1974-01-01
The formalism for studying perturbations of a triaxial rigid body within the Hamilton-Jacobi framework is developed. The motion of a triaxial artificial earth satellite about its center of mass is studied. Variables are found which permit separation, and the Euler angles and associated conjugate momenta are obtained as functions of canonical constants and time.
Amel'kin, N. I.
2011-01-01
Equations of motion are obtained for a rigid body bearing N three-degree-of-freedom control momentum gyroscopes in gimbals and the entire set of steady motions in a homogeneous external field is determined. The steady motion dependence on the magnitude of the system angular momentum is studied and a
Lajimi, Seyed Amir Mousavi
2014-01-01
The nonlinear dynamics of a microbeam-rigid body gyroscope are investigated by using a continuation method. To study the nonlinear dynamics of the system, the Lagrangian of the system is discretized and the reduced-order model is obtained. By using the continuation method, the frequency-response curves are computed and the stability of response is determined.
Liu, Chi; Qiu, Yi; Griffin, Michael J
2017-08-16
Biodynamic responses of the seated human body are usually measured and modelled assuming a single point of vibration excitation. With vertical vibration excitation, this study investigated how forces are distributed over the body-seat interface. Vertical and fore-and-aft forces were measured beneath the ischial tuberosities, middle thighs, and front thighs of 14 subjects sitting on a rigid flat seat in three postures with different thigh contact while exposed to random vertical vibration at three magnitudes. Measures of apparent mass were calculated from transfer functions between the vertical acceleration of the seat and the vertical or fore-and-aft forces measured at the three locations, and the sum of these forces. When sitting normally or sitting with a high footrest, vertical forces at the ischial tuberosities dominated the vertical apparent mass. With feet unsupported to give increased thigh contact, vertical forces at the front thighs were dominant around 8Hz. Around 3-7Hz, fore-and-aft forces at the middle thighs dominated the fore-and-aft cross-axis apparent mass. Around 8-10Hz, fore-and-aft forces were dominant at the ischial tuberosities with feet supported but at the front thighs with feet unsupported. All apparent masses were nonlinear: as the vibration magnitude increased the resonance frequencies decreased. With feet unsupported, the nonlinearity in the apparent mass was greater at the front thighs than at the ischial tuberosities. It is concluded that when the thighs are supported on a seat it is not appropriate to assume the body has a single point of vibration excitation. Copyright © 2017 Elsevier Ltd. All rights reserved.
A navigator-based rigid body motion correction for magnetic resonance imaging
Energy Technology Data Exchange (ETDEWEB)
Ullisch, Marcus Goerge
2012-01-24
A novel three-dimensional navigator k-space trajectory for rigid body motion detection for Magnetic Resonance Imaging (MRI) - the Lissajous navigator - was developed and quantitatively compared to the existing spherical navigator trajectory [1]. The spherical navigator cannot sample the complete spherical surface due to slew rate limitations of the scanner hardware. By utilizing a two dimensional Lissajous figure which is projected onto the spherical surface, the Lissajous navigator overcomes this limitation. The complete sampling of the sphere consequently leads to rotation estimates with higher and more isotropic accuracy. Simulations and phantom measurements were performed for both navigators. Both simulations and measurements show a significantly higher overall accuracy of the Lissajous navigator and a higher isotropy of the rotation estimates. Measured under identical conditions with identical postprocessing, the measured mean absolute error of the rotation estimates for the Lissajous navigator was 38% lower (0.3 ) than for the spherical navigator (0.5 ). The maximum error of the Lissajous navigator was reduced by 48% relative to the spherical navigator. The Lissajous navigator delivers higher accuracy of rotation estimation and a higher degree of isotropy than the spherical navigator with no evident drawbacks; these are two decisive advantages, especially for high-resolution anatomical imaging.
Aoun, Bachir
2016-05-01
A new Reverse Monte Carlo (RMC) package "fullrmc" for atomic or rigid body and molecular, amorphous, or crystalline materials is presented. fullrmc main purpose is to provide a fully modular, fast and flexible software, thoroughly documented, complex molecules enabled, written in a modern programming language (python, cython, C and C++ when performance is needed) and complying to modern programming practices. fullrmc approach in solving an atomic or molecular structure is different from existing RMC algorithms and software. In a nutshell, traditional RMC methods and software randomly adjust atom positions until the whole system has the greatest consistency with a set of experimental data. In contrast, fullrmc applies smart moves endorsed with reinforcement machine learning to groups of atoms. While fullrmc allows running traditional RMC modeling, the uniqueness of this approach resides in its ability to customize grouping atoms in any convenient way with no additional programming efforts and to apply smart and more physically meaningful moves to the defined groups of atoms. In addition, fullrmc provides a unique way with almost no additional computational cost to recur a group's selection, allowing the system to go out of local minimas by refining a group's position or exploring through and beyond not allowed positions and energy barriers the unrestricted three dimensional space around a group.
A simple molecular mechanics integrator in mixed rigid body and dihedral angle space
Energy Technology Data Exchange (ETDEWEB)
Vitalis, Andreas, E-mail: a.vitalis@bioc.uzh.ch [Department of Biochemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich (Switzerland); Pappu, Rohit V. [Department of Biomedical Engineering and Center for Biological Systems Engineering, Washington University in St. Louis, One Brookings Drive, Campus Box 1097, St. Louis, Missouri 63130 (United States)
2014-07-21
We propose a numerical scheme to integrate equations of motion in a mixed space of rigid-body and dihedral angle coordinates. The focus of the presentation is biomolecular systems and the framework is applicable to polymers with tree-like topology. By approximating the effective mass matrix as diagonal and lumping all bias torques into the time dependencies of the diagonal elements, we take advantage of the formal decoupling of individual equations of motion. We impose energy conservation independently for every degree of freedom and this is used to derive a numerical integration scheme. The cost of all auxiliary operations is linear in the number of atoms. By coupling the scheme to one of two popular thermostats, we extend the method to sample constant temperature ensembles. We demonstrate that the integrator of choice yields satisfactory stability and is free of mass-metric tensor artifacts, which is expected by construction of the algorithm. Two fundamentally different systems, viz., liquid water and an α-helical peptide in a continuum solvent are used to establish the applicability of our method to a wide range of problems. The resultant constant temperature ensembles are shown to be thermodynamically accurate. The latter relies on detailed, quantitative comparisons to data from reference sampling schemes operating on exactly the same sets of degrees of freedom.
Parker, Jason G; Mair, Bernard A; Gilland, David R
2009-10-01
In this article, a new method is introduced for estimating the motion of the heart due to respiration in gated cardiac SPECT using a rigid-body model with rotation parametrized by a unit quaternion. The method is based on minimizing the sum of squared errors between the reference and the deformed frames resulting from the usual optical flow constraint by using an optimized conjugate gradient routine. This method does not require any user-defined parameters or penalty terms, which simplifies its use in a clinical setting. Using a mathematical phantom, the method was quantitatively compared to the principal axis method, as well as an iterative method in which the rotation matrix was represented by Euler angles. The quaternion-based method was shown to be substantially more accurate and robust across a wide range of extramyocardial activity levels than the principal axis method. Compared with the Euler angle representation, the quaternion-based method resulted in similar accuracy but a significant reduction in computation times. Finally, the quaternion-based method was investigated using a respiratory-gated cardiac SPECT acquisition of a human subject. The motion-corrected image has increased sharpness and myocardial uniformity compared to the uncorrected image.
Periodic contact between piezoelectric materials and a rigid body with a wavy surface
Zhou, Yue-Ting; Kim, Tae-Won
2015-01-01
An exact analysis is conducted for periodic, two-dimensional (2D) contact of piezoelectric materials in contact with a rigid body with a wavy surface pressed by uniform stresses at infinity. For three cases of eigenvalue distribution, three harmonic functions automatically satisfying the periodicity conditions are carefully constructed to facilitate the derivation of the solution of the considered problem. The stresses and electric displacements are obtained as infinite series. It is found that for the full contact case, the disturbance stress and electric displacement fields remain only the first harmonic which has the slowest decay in the y-direction. The convergence behaviours of the infinite series are checked, which shows that the external loading p and different positions have a great effect on the convergence behaviours of the infinite series and 400 terms are enough to get accurate solution at each position. Numerical results are presented to justify the validity of the present derivation and show the effect of the external loading on the contact behaviours.
Rigid body dynamics modeling, experimental characterization, and performance analysis of a howitzer
Institute of Scientific and Technical Information of China (English)
Nachiketa TIWARI; Mukund PATIL; Ravi SHANKAR; Abhishek SARASWAT; Rituraj DWIVEDI
2016-01-01
A large caliber howitzer is a complex and cumbersome assembly. Understanding its dynamics and performance attributes’ sensitivity to changes in its design parameters can be a very time-consuming and expensive exercise, as such an effort requires highly sophisticated test rigs and platforms. However, the need of such an understanding is crucially important for system designers, users, and evaluators. Some of the key performance attributes of such a system are its vertical jump, forward motion, recoil displacement, and force transmitted to ground through tires and trail after the gun has been fired. In this work, we have developed a rigid body dynamics model for a representative howitzer system, and used relatively simple experimental procedures to estimate its principal design parameters. Such procedures can help in obviating the need of expensive experimental rigs, especially in early stages of the design cycle. These parameters were subsequently incorporated into our simulation model, which was then used to predict gun performance. Finally, we conducted several sensitivity studies to understand the influence of changes in various design parameters on system performance. Their results provide useful insights in our understanding of the functioning of the overall system.
Generalized Predictive Control of Dynamic Systems with Rigid-Body Modes
Kvaternik, Raymond G.
2013-01-01
Numerical simulations to assess the effectiveness of Generalized Predictive Control (GPC) for active control of dynamic systems having rigid-body modes are presented. GPC is a linear, time-invariant, multi-input/multi-output predictive control method that uses an ARX model to characterize the system and to design the controller. Although the method can accommodate both embedded (implicit) and explicit feedforward paths for incorporation of disturbance effects, only the case of embedded feedforward in which the disturbances are assumed to be unknown is considered here. Results from numerical simulations using mathematical models of both a free-free three-degree-of-freedom mass-spring-dashpot system and the XV-15 tiltrotor research aircraft are presented. In regulation mode operation, which calls for zero system response in the presence of disturbances, the simulations showed reductions of nearly 100%. In tracking mode operations, where the system is commanded to follow a specified path, the GPC controllers produced the desired responses, even in the presence of disturbances.
Rigid body dynamics modeling, experimental characterization, and performance analysis of a howitzer
Directory of Open Access Journals (Sweden)
Nachiketa Tiwari
2016-12-01
Full Text Available A large caliber howitzer is a complex and cumbersome assembly. Understanding its dynamics and performance attributes' sensitivity to changes in its design parameters can be a very time-consuming and expensive exercise, as such an effort requires highly sophisticated test rigs and platforms. However, the need of such an understanding is crucially important for system designers, users, and evaluators. Some of the key performance attributes of such a system are its vertical jump, forward motion, recoil displacement, and force transmitted to ground through tires and trail after the gun has been fired. In this work, we have developed a rigid body dynamics model for a representative howitzer system, and used relatively simple experimental procedures to estimate its principal design parameters. Such procedures can help in obviating the need of expensive experimental rigs, especially in early stages of the design cycle. These parameters were subsequently incorporated into our simulation model, which was then used to predict gun performance. Finally, we conducted several sensitivity studies to understand the influence of changes in various design parameters on system performance. Their results provide useful insights in our understanding of the functioning of the overall system.
Hamilton, H. Harris, II; Millman, Daniel R.; Greendyke, Robert B.
1992-01-01
A computer code was developed that uses an implicit finite-difference technique to solve nonsimilar, axisymmetric boundary layer equations for both laminar and turbulent flow. The code can treat ideal gases, air in chemical equilibrium, and carbon tetrafluoride (CF4), which is a useful gas for hypersonic blunt-body simulations. This is the only known boundary layer code that can treat CF4. Comparisons with experimental data have demonstrated that accurate solutions are obtained. The method should prove useful as an analysis tool for comparing calculations with wind tunnel experiments and for making calculations about flight vehicles where equilibrium air chemistry assumptions are valid.
Zoby, E. V.; Graves, R. A., Jr.
1973-01-01
A method for the rapid calculation of the inviscid shock layer about blunt axisymmetric bodies at an angle of attack of 0 deg has been developed. The procedure is of an inverse nature, that is, a shock wave is assumed and calculations proceed along rays normal to the shock. The solution is iterated until the given body is computed. The flow field solution procedure is programed at the Langley Research Center for the Control Data 6600 computer. The geometries specified in the program are sphores, ellipsoids, paraboloids, and hyperboloids which may conical afterbodies. The normal momentum equation is replaced with an approximate algebraic expression. This simplification significantly reduces machine computation time. Comparisons of the present results with shock shapes and surface pressure distributions obtained by the more exact methods indicate that the program provides reasonably accurate results for smooth bodies in axisymmetric flow. However, further research is required to establish the proper approximate form of the normal momentum equation for the two-dimensional case.
Zabolotnov, Yu. M.
2016-07-01
We analyze the spatial motion of a rigid body fixed to a cable about its center of mass when the orbital cable system is unrolling. The analysis is based on the integral manifold method, which permits separating the rigid body motion into the slow and fast components. The motion of the rigid body is studied in the case of slow variations in the cable tension force and under the action of various disturbances.We estimate the influence of the static and dynamic asymmetry of the rigid body on its spatial motion about the cable fixation point. An example of the analysis of the rigid body motion when the orbital cable system is unrolling is given for a special program of variations in the cable tension force. The conditions of applicability of the integral manifold method are analyzed.
DEFF Research Database (Denmark)
Deriabine, Mikhail
2003-01-01
We consider the problem of heavy rigid body dynamics in an infinite volume of an ideal incompressible fluid performing a potential motion. If the body is axially-symmetric, then the system admits partial solutions, when the axis of symmetry is vertical, and the body sinks and rotates around its...... symmetry axis. These solutions were found by V.A.Steklov already at the end of the 19th century, and he also pointed out that in general these motions are unstable (as they are uniformly accelerated).Here we consider the more delicate question, namely we derive the conditions for stability of the rotation...
Acoustic equations for a gas stream in rigid-body rotation
Garcia-Ybarra, Pedro L.; Marin-Antuña, Jose M.
2017-02-01
The classical topic of wave propagation in a rotating gas is revisited by deducing scalar wave equations for propagation of acoustic and rotational waves through a plug flow of gas in rigid-body rotation with arbitrary intensities of the radial stratification. In the light of these novel equations, wave propagation is analyzed in two different base gas states: isothermal and homentropic. In both cases, previous findings are recovered that assess the validity of the equations and new results are established. In the non-homentropic but isothermal case, the set of governing equations is reduced to two coupled scalar wave equations with space dependent coefficients for the disturbances of density and pressure. Travelling wave solutions with variable amplitude have been obtained in the limit of weak stratification both for inertial waves as for acoustic waves which, in general, propagate on different frequency bands that overlap in the small wavenumber region. Furthermore, the entropy stratification in the base state is stable and compels the propagation of internal waves, leading to hybrid acoustic-inertial-vortical modes. In the homentropic case, the adiabatic relation between pressure and density disturbances allows to reduce further the governing equations to a single fourth-order scalar wave equation. In this case, the sound propagation velocity depends on the distance to the rotation axis and solutions are found by multiple-scale analyses in the form of waves with slowly varying amplitude and wavenumber. The corresponding eikonal equation shows that acoustic rays are refracted towards the rotation axis, propagating and spinning along and around it. In that way, the swirling gas behaves as an axial waveguide trapping inside any acoustic ray propagating in the vortex with large enough azimuthal and/or vertical wavenumber component.
Directory of Open Access Journals (Sweden)
Xiaojia Xiang
2015-01-01
Full Text Available The collocation method is extended to the special orthogonal group SO(3 with application to optimal attitude control (OAC of a rigid body. A left-invariant rigid-body attitude dynamical model on SO(3 is established. For the left invariance of the attitude configuration equation in body-fixed frame, a geometrically exact numerical method on SO(3, referred to as the geometric collocation method, is proposed by deriving the equivalent Lie algebra equation in so(3 of the left-invariant configuration equation. When compared with the general Gauss pseudo-spectral method, the explicit RKMK, and Lie group variational integrator having the same order and stepsize in numerical tests for evolving a free-floating rigid-body attitude dynamics, the proposed method is higher in accuracy, time performance, and structural conservativeness. In addition, the numerical method is applied to solve a constrained OAC problem on SO(3. The optimal control problem is transcribed into a nonlinear programming problem, in which the equivalent Lie algebra equation is being considered as the defect constraints instead of the configuration equation. The transcription method is coordinate-free and does not need chart switching or special handling of singularities. More importantly, with the numerical advantage of the geometric collocation method, the proposed OAC method may generate satisfying convergence rate.
Reaungamornrat, S.; Wang, A. S.; Uneri, A.; Otake, Y.; Zhao, Z.; Khanna, A. J.; Siewerdsen, J. H.
2014-03-01
Purpose: Deformable registration of preoperative and intraoperative images facilitates accurate localization of target and critical anatomy in image-guided spine surgery. However, conventional deformable registration fails to preserve the morphology of rigid bone anatomy and can impart distortions that confound high-precision intervention. We propose a constrained registration method that preserves rigid morphology while allowing deformation of surrounding soft tissues. Method: The registration method aligns preoperative 3D CT to intraoperative cone-beam CT (CBCT) using free-form deformation (FFD) with penalties on rigid body motion imposed according to a simple intensity threshold. The penalties enforced 3 properties of a rigid transformation - namely, constraints on affinity (AC), orthogonality (OC), and properness (PC). The method also incorporated an injectivity constraint (IC) to preserve topology. Physical experiments (involving phantoms, an ovine spine, and a human cadaver) as well as digital simulations were performed to evaluate the sensitivity to registration parameters, preservation of rigid body morphology, and overall registration accuracy of constrained FFD in comparison to conventional unconstrained FFD (denoted uFFD) and Demons registration. Result: FFD with orthogonality and injectivity constraints (denoted FFD+OC+IC) demonstrated improved performance compared to uFFD and Demons. Affinity and properness constraints offered little or no additional improvement. The FFD+OC+IC method preserved rigid body morphology at near-ideal values of zero dilatation (D = 0.05, compared to 0.39 and 0.56 for uFFD and Demons, respectively) and shear (S = 0.08, compared to 0.36 and 0.44 for uFFD and Demons, respectively). Target registration error (TRE) was similarly improved for FFD+OC+IC (0.7 mm), compared to 1.4 and 1.8 mm for uFFD and Demons. Results were validated in human cadaver studies using CT and CBCT images, with FFD+OC+IC providing excellent preservation
Slaughter, Chris; Bagwell, Justin; Checkles, Costa; Sentis, Luis; Vishwanath, Sriram
2011-01-01
Motivated by an emerging theory of robust low-rank matrix representation, in this paper, we introduce a novel solution for online rigid-body motion registration. The goal is to develop algorithmic techniques that enable a robust, real-time motion registration solution suitable for low-cost, portable 3-D camera devices. Assuming 3-D image features are tracked via a standard tracker, the algorithm first utilizes Robust PCA to initialize a low-rank shape representation of the rigid body. Robust PCA finds the global optimal solution of the initialization, while its complexity is comparable to singular value decomposition. In the online update stage, we propose a more efficient algorithm for sparse subspace projection to sequentially project new feature observations onto the shape subspace. The lightweight update stage guarantees the real-time performance of the solution while maintaining good registration even when the image sequence is contaminated by noise, gross data corruption, outlying features, and missing ...
Directory of Open Access Journals (Sweden)
Jeng Hei Chow
2016-07-01
Full Text Available An implicit method of solving the six degree-of-freedom rigid body motion equations based on the second order Adams-Bashforth-Moulten method was utilised as an improvement over the leapfrog scheme by making modifications to the rigid body motion solver libraries directly. The implementation will depend on predictor-corrector steps still residing within the hybrid Pressure Implicit with Splitting of Operators - Semi-Implicit Method for Pressure Linked Equations (PIMPLE outer corrector loops to ensure strong coupling between fluid and motion. Aitken's under-relaxation is also introduced in this study to optimise the convergence rate and stability of the coupled solver. The resulting coupled solver ran on a free floating object tutorial test case when converged matches the original solver. It further allows a varying 70%–80% reduction in simulation times compared using a fixed under-relaxation to achieve the required stability.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Impact dynamics of multi-rigid-body systems with joint friction is considered.Based on the traditional approximate assumption dealing with impact problem, a general numerical method called the sliding state stepping algorithm is introduced. This method can avoid difficulties in solving differential equations with variable scale and its result can avoid energy inconsistency before and after impact from considering complexily of tangential sliding mode. An example is given to describe details using this algorithm.
A vector-dyadic development of the equations of motion for N-coupled rigid bodies and point masses
Frisch, H. P.
1974-01-01
The equations of motion are derived, in vector-dyadic format, for a topological tree of coupled rigid bodies, point masses, and symmetrical momentum wheels. These equations were programmed, and form the basis for the general-purpose digital computer program N-BOD. A complete derivation of the equations of motion is included along with a description of the methods used for kinematics, constraint elimination, and for the inclusion of nongyroscope forces and torques acting external or internal to the system.
Lācis, Uǧis; Bagheri, Shervin
2015-01-01
Dispersion of low-density rigid particles with complex geometries is ubiquitous in both natural and industrial environments. We show that while explicit methods for coupling the incompressible Navier-Stokes equations and Newton's equations of motion are often sufficient to solve for the motion of cylindrical particles with low density ratios, for more complex particles - such as a body with a protrusion - they become unstable. We present an implicit formulation of the coupling between rigid body dynamics and fluid dynamics within the framework of the immersed boundary projection method. Similar to previous work on this method, the resulting matrix equation in the present approach is solved using a block-LU decomposition. Each step of the block-LU decomposition is modified to incorporate the rigid body dynamics. We show that our method achieves second-order accuracy in space and first-order in time (third-order for practical settings), only with a small additional computational cost to the original method. Our...
Pickl, Kristina; Iglberger, Klaus; Pande, Jayant; Mecke, Klaus; Smith, Ana-Suncana; Rüde, Ulrich
2011-01-01
We simulate the self-propulsion of devices in a fluid in the regime of low Reynolds numbers. Each device consists of three bodies (spheres or capsules) connected with two damped harmonic springs. Sinusoidal driving forces compress the springs which are resolved within a rigid body physics engine. The latter is consistently coupled to a 3D lattice Boltzmann framework for the fluid dynamics. In simulations of three-sphere devices, we find that the propulsion velocity agrees well with theoretical predictions. In simulations where some or all spheres are replaced by capsules, we find that the asymmetry of the design strongly affects the propelling efficiency.
Romano, Marcello
2012-01-01
New exact analytic solutions are introduced for the rotational motion of a rigid body having two equal principal moments of inertia and subjected to an external torque which is constant in magnitude. In particular, the solutions are obtained for the following cases: (1) Torque parallel to the symmetry axis and arbitrary initial angular velocity; (2) Torque perpendicular to the symmetry axis and such that the torque is rotating at a constant rate about the symmetry axis, and arbitrary initial angular velocity; (3) Torque and initial angular velocity perpendicular to the symmetry axis, with the torque being fixed with the body. In addition to the solutions for these three forced cases, an original solution is introduced for the case of torque-free motion, which is simpler than the classical solution as regards its derivation and uses the rotation matrix in order to describe the body orientation. This paper builds upon the recently discovered exact solution for the motion of a rigid body with a spherical ellipso...
Xiao, Di; Zahra, David; Bourgeat, Pierrick; Berghofer, Paula; Acosta Tamayo, Oscar; Wimberley, Catriona; Gregoire, Marie C.; Salvado, Olivier
2011-03-01
Small animal image registration is challenging because of its joint structure, and posture and position difference in each acquisition without a standard scan protocol. In this paper, we face the issue of mouse whole-body skeleton registration from CT images. A novel method is developed for analyzing mouse hind-limb and fore-limb postures based on geodesic path descriptor and then registering the major skeletons and fore limb skeletons initially by thin-plate spline (TPS) transform based on the obtained geodesic paths and their enhanced correspondence fields. A target landmark correction method is proposed for improving the registration accuracy of the improved 3D shape context non-rigid registration method we previously proposed. A novel non-rigid registration framework, combining the skeleton posture analysis, geodesic path based initial alignment and 3D shape context model, is proposed for mouse whole-body skeleton registration. The performance of the proposed methods and framework was tested on 12 pairs of mouse whole-body skeletons. The experimental results demonstrated the flexibility, stability and accuracy of the proposed framework for automatic mouse whole body skeleton registration.
Flutter Analysis of RX-420 Balistic Rocket Fin Involving Rigid Body Modes of Rocket Structures
Novi Andria
2013-01-01
Flutter is a phenomenon that has brought a catastrophic failure to the flight vehicle structure. In this experiment, flutter was analyzed for its symmetric and antisymmetric configuration to understand the effect of rocket rigid modes to the fin flutter characteristic. This research was also expected to find out the safety level of RX-420 structure design. The analysis was performed using half rocket model. Fin structure used in this research was a fin which has semispan 600 mm, thickness 12 ...
Self-propulsion of a body with rigid surface and variable coefficient of lift in a perfect fluid
Ramodanov, Sergey M.; Tenenev, Valentin A.; Treschev, Dmitry V.
2012-11-01
We study the system of a 2D rigid body moving in an unbounded volume of incompressible, vortex-free perfect fluid which is at rest at infinity. The body is equipped with a gyrostat and a so-called Flettner rotor. Due to the latter the body is subject to a lifting force (Magnus effect). The rotational velocities of the gyrostat and the rotor are assumed to be known functions of time (control inputs). The equations of motion are presented in the form of the Kirchhoff equations. The integrals of motion are given in the case of piecewise continuous control. Using these integrals we obtain a (reduced) system of first-order differential equations on the configuration space. Then an optimal control problem for several types of the inputs is solved using genetic algorithms.
Dobson, G. J.
1998-07-01
Newton's treatment of the precession of the equinoxes in his Philosophiae Naturalis Principia Mathematica was recognised by d'Alembert in 1749 as being faulty, despite the very close agreement between Newton's calculated value for the rate of precesion and the observed value. Here, the author presents an analysis of Newton's geometrical methods applied in his treatment of precession and claims that it was basically flawed because Newton lacked knowledge of the principles of rigid body dynamics and, in particular, was unaware of the idea of angular momentum.
Separation of Target Rigid Body and Micro-Doppler Effects in ISAR/SAR Imaging
2006-09-01
returned from the surface of the vehicle. From micro-Doppler modulations in the engine vibration signal, one can distinguish whether it is a gas turbine...v~hicule peuvent ýtre d~tect~es par des signaux radars r~fl~chis d la surface du v~hicule. Ak partir de mo- dulations micro-Doppler du signal de...fenetre large uine forte concentration du signal correspondant aux parties du corps rigide. La deuxi~me technique se fonide sur le traitement des
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Svetoslav Ganchev Nikolov
2015-07-01
Full Text Available The study of the dynamic behavior of a rigid body with one fixed point (gyroscope has a long history. A number of famous mathematicians and mechanical engineers have devoted enormous time and effort to clarify the role of dynamic effects on its movement (behavior – stable, periodic, quasi-periodic or chaotic. The main objectives of this review are: 1 to outline the characteristic features of the theory of dynamical systems and 2 to reveal the specific properties of the motion of a rigid body with one fixed point (gyroscope.This article consists of six sections. The first section addresses the main concepts of the theory of dynamical systems. Section two presents the main theoretical results (obtained so far concerning the dynamic behavior of a solid with one fixed point (gyroscope. Section three examines the problem of gyroscopic stabilization. Section four deals with the non-linear (chaotic dynamics of the gyroscope. Section five is a brief analysis of the gyroscope applications in engineering. The final section provides conclusions and generalizations on why the theory of dynamical systems should be used in the study of the movement of gyroscopic systems.
Stability of the classical type of relative equilibria of a rigid body in the J2 problem
Wang, Yue
2013-01-01
The motion of a point mass in the J2 problem is generalized to that of a rigid body in a J2 gravity field. The linear and nonlinear stability of the classical type of relative equilibria of the rigid body, which have been obtained in our previous paper, are studied in the framework of geometric mechanics with the second-order gravitational potential. Non-canonical Hamiltonian structure of the problem, i.e., Poisson tensor, Casimir functions and equations of motion, are obtained through a Poisson reduction process by means of the symmetry of the problem. The linear system matrix at the relative equilibria is given through the multiplication of the Poisson tensor and Hessian matrix of the variational Lagrangian. Based on the characteristic equation of the linear system matrix, the conditions of linear stability of the relative equilibria are obtained. The conditions of nonlinear stability of the relative equilibria are derived with the energy-Casimir method through the projected Hessian matrix of the variationa...
Bhalla, Amneet Pal Singh; Bale, Rahul; Griffith, Boyce E.; Patankar, Neelesh A.
2013-10-01
Many problems of interest in biological fluid mechanics involve interactions between fluids and solids that require the coupled solution of momentum equations for both the fluid and the solid. In this work, we develop a mathematical framework and an adaptive numerical method for such fluid-structure interaction (FSI) problems in which the structure may be rigid, deforming, or elastic. We employ an immersed boundary (IB) formulation of the problem that permits us to avoid body conforming discretizations and to use fast Cartesian grid solvers. Rigidity and deformational kinematic constraints are imposed using a formulation based on distributed Lagrange multipliers, and a conventional IB method is used to describe the elasticity of the immersed body. We use Cartesian grid adaptive mesh refinement (AMR) to discretize the equations of motion and thereby obtain a solution methodology that efficiently captures thin boundary layers at fluid-solid interfaces as well as flow structures shed from such interfaces. This adaptive methodology is validated for several benchmark problems in two and three spatial dimensions. In addition, we use this scheme to simulate free swimming, including the maneuvering of a two-dimensional model eel and a three-dimensional model of the weakly electric black ghost knifefish.
Andreani, Roberto; Friedlander, Ana; Mello, Margarida P.; Santos, Sandra A.
2005-06-01
In this work we show that the mixed nonlinear complementarity problem may be formulated as an equivalent nonlinear bound-constrained optimization problem that preserves the smoothness of the original data. One may thus take advantage of existing codes for bound-constrained optimization. This approach is implemented and tested by means of an extensive set of numerical experiments, showing promising results. The mixed nonlinear complementarity problems considered in the tests arise from the discretization of a motion planning problem concerning a set of rigid 3D bodies in contact in the presence of friction. We solve the complementarity problem associated with a single time frame, thus calculating the contact forces and accelerations of the bodies involved.
An integral equation formulation for rigid bodies in Stokes flow in three dimensions
Corona, Eduardo; Greengard, Leslie; Rachh, Manas; Veerapaneni, Shravan
2017-03-01
We present a new derivation of a boundary integral equation (BIE) for simulating the three-dimensional dynamics of arbitrarily-shaped rigid particles of genus zero immersed in a Stokes fluid, on which are prescribed forces and torques. Our method is based on a single-layer representation and leads to a simple second-kind integral equation. It avoids the use of auxiliary sources within each particle that play a role in some classical formulations. We use a spectrally accurate quadrature scheme to evaluate the corresponding layer potentials, so that only a small number of spatial discretization points per particle are required. The resulting discrete sums are computed in O (n) time, where n denotes the number of particles, using the fast multipole method (FMM). The particle positions and orientations are updated by a high-order time-stepping scheme. We illustrate the accuracy, conditioning and scaling of our solvers with several numerical examples.
Precession of a Freely Rotating Rigid Body Inelastic Relaxation in the Vicinity of Poles
Efroimsky, M
1999-01-01
When a solid body is freely rotating at an angular velocity ${\\bf \\Omega}$, the ellipsoid of constant angular momentum, in the space $\\Omega_1, \\Omega_2, \\Omega_3$, has poles corresponding to spinning about the minimal-inertia and maximal-inertia axes. The first pole may be considered stable if we neglect the inner dissipation, but becomes unstable if the dissipation is taken into account. This happens because the bodies dissipate energy when they rotate about any axis different from that of the maximal inertia. In the case of an oblate symmetrical body, the angular velocity describes a circular cone about the vector of (conserved) angular momentum. In the course of relaxation, the angle of this cone decreases, so that both the angular velocity and the maximal-inertia axis of the body align along the angular momentum. The generic case of an asymmetric body is far more involved. Even the symmetrical prolate body exhibits a sophisticated behaviour, because an infinitesimally small deviation of the body's shape ...
Guan, P. B.; Tingatinga, E. A.; Longalong, R. E.; Saguid, J.
2016-09-01
During the past decades, the complexity of conventional methods to perform seismic performance assessment of buildings led to the development of more effective approaches. The rigid body spring-discrete element method (RBS-DEM) is one of these approaches and has recently been applied to the study of the behavior of reinforced concrete (RC) buildings subjected to strong earthquakes. In this paper, the governing equations of RBS-DEM planar elements subjected to lateral loads and horizontal ground motion are presented and used to replicate the hysteretic behavior of experimental RC columns. The RBS-DEM models of columns are made up of rigid components connected by systems of springs that simulate axial, shear, and bending behavior of an RC section. The parameters of springs were obtained using Response-2000 software and the hysteretic response of the models of select columns from the Pacific Earthquake Engineering Research (PEER) Structural Performance Database were computed numerically. Numerical examples show that one-component models were able to simulate the initial stiffness reasonably, while the displacement capacity of actual columns undergoing large displacements were underestimated.
Flutter Analysis of RX-420 Balistic Rocket Fin Involving Rigid Body Modes of Rocket Structures
Directory of Open Access Journals (Sweden)
Novi Andria
2013-03-01
Full Text Available Flutter is a phenomenon that has brought a catastrophic failure to the flight vehicle structure. In this experiment, flutter was analyzed for its symmetric and antisymmetric configuration to understand the effect of rocket rigid modes to the fin flutter characteristic. This research was also expected to find out the safety level of RX-420 structure design. The analysis was performed using half rocket model. Fin structure used in this research was a fin which has semispan 600 mm, thickness 12 mm, chord root 700 mm, chord tip 400 mm, made by Al 6061-T651, double spar configuration with skin thickness of 2 mm. Structural dynamics and flutter stability were analyzed using finite element software implemented on MSC. Nastran. The analysis shows that the antisymmetric flutter mode is more critical than symmetric flutter mode. At sea level altitude, antisymmetric flutter occurs at 6.4 Mach, and symmetric flutter occurs at 10.15 Mach. Compared to maximum speed of RX-420 which is 4.5 Mach at altitude 11 km or equivalent to 2.1 Mach at sea level, it can be concluded that the RX-420 structure design is safe, and flutter will not occur during flight.
The Advanced Part of a Treatise on the Dynamics of a System of Rigid Bodies
Routh, Edward John
2013-03-01
Preface; 1. Moving axes and relative motion; 2. Oscillations about equilibrium; 3. Oscillations about a state of motion; 4. Motion of a body under no forces; 5. Motion of a body under any forces; 6. Nature of the motion given by linear equations and the conditions of stability; 7. Free and forced oscillations; 8. Determination of the constants of integration in terms of the initial conditions; 9. Calculus of finite differences; 10. Calculus of variations; 11. Precession and nutation; 12. Motion of the moon about its centre; 13. Motion of a string or chain; 14. Motion of a membrane; Notes.
Pandurangan, Arun Prasad; Topf, Maya
2012-09-15
To better analyze low-resolution cryo electron microscopy maps of macromolecular assemblies, component atomic structures frequently have to be flexibly fitted into them. Reaching an optimal fit and preventing the fitting process from getting trapped in local minima can be significantly improved by identifying appropriate rigid bodies (RBs) in the fitted component. Here we present the RIBFIND server, a tool for identifying RBs in protein structures. The server identifies RBs in proteins by calculating spatial proximity between their secondary structural elements. The RIBFIND web server and its standalone program are available at http://ribfind.ismb.lon.ac.uk. a.pandurangan@mail.cryst.bbk.ac.uk Supplementary data are available at Bioinformatics online.
Hagelueken, Gregor; Abdullin, Dinar; Ward, Richard; Schiemann, Olav
2013-10-01
Nanometer distance measurements based on electron paramagnetic resonance methods in combination with site-directed spin labelling are powerful tools for the structural analysis of macromolecules. The software package mtsslSuite provides scientists with a set of tools for the translation of experimental distance distributions into structural information. The package is based on the previously published mtsslWizard software for in silico spin labelling. The mtsslSuite includes a new version of MtsslWizard that has improved performance and now includes additional types of spin labels. Moreover, it contains applications for the trilateration of paramagnetic centres in biomolecules and for rigid-body docking of subdomains of macromolecular complexes. The mtsslSuite is tested on a number of challenging test cases and its strengths and weaknesses are evaluated.
A boundary integral approach to analyze the viscous scattering of a pressure wave by a rigid body
Homentcovschi, Dorel; Miles, Ronald N.
2008-01-01
The paper provides boundary integral equations for solving the problem of viscous scattering of a pressure wave by a rigid body. By using this mathematical tool uniqueness and existence theorems are proved. Since the boundary conditions are written in terms of velocities, vector boundary integral equations are obtained for solving the problem. The paper introduces single-layer viscous potentials and also a stress tensor. Correspondingly, a viscous double-layer potential is defined. The properties of all these potentials are investigated. By representing the scattered field as a combination of a single-layer viscous potential and a double-layer viscous potential the problem is reduced to the solution of a singular vectorial integral equation of Fredholm type of the second kind. In the case where the stress vector on the boundary is the main quantity of interest the corresponding boundary singular integral equation is proved to have a unique solution. PMID:18709178
Homentcovschi, Dorel
2008-01-01
This paper gives a regular vector boundary integral equation for solving the problem of viscous scattering of a pressure wave by a rigid body. Firstly, single-layer viscous potentials and a generalized stress tensor are introduced. Correspondingly, generalized viscous double-layer potentials are defined. By representing the scattered field as a combination of a single-layer viscous potential and a generalized viscous double-layer potential, the problem is reduced to the solution of a vectorial Fredholm integral equation of the second kind. Generally, the vector integral equation is singular. However, there is a particular stress tensor, called pseudostress, which yields a regular integral equation. In this case, the Fredholm alternative applies and permits a direct proof of the existence and uniqueness of the solution. The results presented here provide the foundation for a numerical solution procedure. PMID:19865494
Institute of Scientific and Technical Information of China (English)
JianhuaCHENG; JunfengLI; 等
1996-01-01
In this paper a mnechanical system is studied in which a rotor rotates around a fixed axis with a string suspended symmetric rigid body.All relative equilibrium strates and their stability are discussed.Considering the spinning angular velocity ω around the fixed vertical axis as a parameter,algebraic equations with this parameter are obtained,Every solution of the equations is relevant to a relative equilibrium state of the system.The existence of two important relative equilibrium states is discussed by numerical method developed in bifurcation theory in this paper,In addition,The lagrange's Theorem is used to determine the stability of the relative equilibrium state relevant to the solution of the algebraic equations.
Knowledge-in-action: a study on the integration of forces and energy in a rigid body
Directory of Open Access Journals (Sweden)
Consuelo Escudero
2009-03-01
Full Text Available This paper intends to go on with the study of problem solving in a compatible way with the theories of conceptual fields (TCC of Vergnaud (1990,1994,1998 and mental models of Johnson-Laird (1983,1990. Together with findings of another study (Escudero & Jaime 2007, some achievements and difficulties of freshmore engineering students when solving problems of the motion of rigid body in terms of the knowledge-in-action are analysed. The research methodology under a qualitative paradigm grouped data into categories which are not provided a priori by the theoretical framework. It can be said that the quality of the conceptual representation has been explicit in the quality of the proposed solution. Some meanings introduced by students in their problem solving activities can be characterized as operational invariants.
回转体垂直入水过程数值模拟%Numerical Simulation of Vertical Water-entry for an Axisymmetric Body
Institute of Scientific and Technical Information of China (English)
王占莹; 王冠军; 尤天庆; 程少华; 林崧
2014-01-01
The numerical simulation of water entry of an axisymmetric body is based on solving the time dependent Reynolds-Averaged Navier-Stokes equations and the VOF multiphase method and the dynamic mesh technique. Numerical results compared favorably with the experimental data show that the numerical method in this paper is able to capture the pressure evolution in the vertical water entry cavity properly, and the hydrodynamic distributions in cavity with various entry speeds are discussed. The study may provide reference and contribute to the engineering design.%针对回转体垂直入水流体动力问题，基于RANS方程、VOF多相流模型和动网格技术进行数值模拟分析，通过试验结果对数值计算模型进行验证，获得垂直入水过程中自由液面及物体表面附着空气泡的发展演化过程，研究回转体不同入水速度对流体动力分布特性的影响，为工程设计提供借鉴与参考。
Geometrical analysis of registration errors in point-based rigid-body registration using invariants.
Shamir, Reuben R; Joskowicz, Leo
2011-02-01
Point-based rigid registration is the method of choice for aligning medical datasets in diagnostic and image-guided surgery systems. The most clinically relevant localization error measure is the Target Registration Error (TRE), which is the distance between the image-defined target and the corresponding target defined on another image or on the physical anatomy after registration. The TRE directly depends on the Fiducial Localization Error (FLE), which is the discrepancy between the selected and the actual (unknown) fiducial locations. Since the actual locations of targets usually cannot be measured after registration, the TRE is often estimated by the Fiducial Registration Error (FRE), which is the RMS distance between the fiducials in both datasets after registration, or with Fitzpatrick's TRE (FTRE) formula. However, low FRE-TRE and FTRE-TRE correlations have been reported in clinical practice and in theoretical studies. In this article, we show that for realistic FLE classes, the TRE and the FRE are uncorrelated, regardless of the target location and the number of fiducials and their configuration, and regardless of the FLE magnitude distribution. We use a geometrical approach and classical invariant theory to model the FLE and derive its relation to the TRE and FRE values. We show that, for these FLE classes, the FTRE and TRE are also uncorrelated. Finally, we show with simulations on clinical data that the FRE-TRE correlation is low also in the neighborhood of the FLE-FRE invariant classes. Consequently, and contrary to common practice, the FRE and FTRE may not always be used as surrogates for the TRE.
Chen, Zhenxian; Zhang, Xuan; Ardestani, Marzieh M; Wang, Ling; Liu, Yaxiong; Lian, Qin; He, Jiankang; Li, Dichen; Jin, Zhongmin
2014-06-01
Lower extremity musculoskeletal computational models play an important role in predicting joint forces and muscle activation simultaneously and are valuable for investigating functional outcomes of the implants. However, current computational musculoskeletal models of total knee replacement rarely consider the bearing surface geometry of the implant. Therefore, these models lack detailed information about the contact loading and joint motion which are important factors for evaluating clinical performances. This study extended a rigid multi-body dynamics simulation of a lower extremity musculoskeletal model to incorporate an artificial knee joint, based upon a novel force-dependent kinematics method, and to characterize the in vivo joint contact mechanics during gait. The developed musculoskeletal total knee replacement model integrated the rigid skeleton multi-body dynamics and the flexible contact mechanics of the tibiofemoral and patellofemoral joints. The predicted contact forces and muscle activations are compared against those in vivo measurements obtained from a single patient with good agreements for the medial contact force (root-mean-square error = 215 N, ρ = 0.96) and lateral contact force (root-mean-square error = 179 N, ρ = 0.75). Moreover, the developed model also predicted the motion of the tibiofemoral joint in all degrees of freedom. This new model provides an important step toward the development of a realistic dynamic musculoskeletal total knee replacement model to predict in vivo knee joint motion and loading simultaneously. This could offer a better opportunity to establish a robust virtual modeling platform for future pre-clinical assessment of knee prosthesis designs, surgical procedures and post-operation rehabilitation.
Analysis of the Gyroscopic Stabilization of a System of Rigid Bodies
DEFF Research Database (Denmark)
Kliem, Wolfhard
1996-01-01
We study the gyroscopic of a three-body system. A new method offinding stability regions, based on mechanism and criteria for gyroscopicstabilization, is presented. Of particular interest in this connection isthe theory of interaction of eigenvalues. This leads to a complete 3-dimensionalanalysis...
Analysis of the gyroscopic stabilization of a system of rigid bodies
DEFF Research Database (Denmark)
Kliem, Wolfhard; Seyranian, Alexander P.
1997-01-01
We study the gyroscopic stability of a three-body system. A new method of finding stability regions, based on mechanism and criteria for gyroscopic stabilization, is presented. Of particular interest in this connection is the theory of interaction of eigenvalues. This leads to a complete 3......-dimensional analysis, which shows the regions of stability, divergence, and flutter of a simple model of a rotating spaceship....
The multivariate analysis of indications of rigid bronchoscopy in suspected foreign body aspiration.
Divarci, E; Toker, B; Dokumcu, Z; Musayev, A; Ozcan, C; Erdener, A
2017-09-01
Foreign body aspiration (FBA) could be a serious life-threatening condition in children. Patients usually underwent bronchoscopy with suspicious of FBA alone. In this study, we aimed to determine which patients need to go to bronchoscopy based on pre-operative findings. Retrospective analysis of patients underwent bronchoscopy between 1999 and 2015 was performed. Clinical symptoms, witnessed aspiration event (WAE), physical examination findings (PEFs) and radiological findings (RFs) were analyzed by multivariate analysis to evaluate the indications of bronchoscopy. 431 patients (266M, 165F) underwent bronchoscopy with a median age of 2 years (7 months-16 years). A foreign body was detected in 68% of the patients. Univariate analysis demonstrated that wheeze was the sole distinctive clinical symptom for detection of FBA (pMultivariate analysis was performed with considering the association between them. The rate of positive bronchoscopy was 91.3% in patients with positive WAE, PEFs and RFs together(84/92). In patients with a positive WAE alone who had not got PEFs and RFs, the rate of positive bronchoscopy was 34.2% (25/73). A foreign body was detected in 84% of the patients who had not got a WAE but positive PEFs and RFs together(21/25). Bronchial laceration was occurred in one patient during bronchoscopy. Pneumothorax was not seen in any of the other patients. The rate of mortality was 0.4% in the overall group (2 patients). The indications of bronchoscopy in suspected FBA are usually based on clinical suspicious. The definition of " suspicous" could be a WAE or positive PEFs and RFs. The association of these factors increase the rate of positive bronchoscopies. In the light of our study, the classical indication for suspected FBA is still valid as "suspicious requires bronchoscopy". Copyright © 2017 Elsevier B.V. All rights reserved.
Konosevich, B. I.
2014-07-01
The error of the Wentzel-Kramers-Brillouin solution of the equations describing the angular motion of the axis of symmetry of rotation of a rigid body (projectile) is estimated. It is established that order of this estimate does not depend on whether the low-frequency oscillations of the axis of symmetry are damped or not
Rupnik, Ewelina; Jansa, Josef
2013-04-01
Central to our investigation is determination of dynamic behaviour of a highly reflective platform floating on water, as well as derivation of parameters defining instantaneous water state. The employed imaging setup consists of three off-the-shelf dSLR cameras capable of video recording at a 30Hz frame rate. In order to observe a change, the non-rigid and non-diffuse bodies impose the adoption of artificial targetting and custom measurement algorithms. Attention will be given to an in-house software tool implemented to carry out point measurement, correspondence search, tracking and outlier detection methods in the presence of specular reflections and a multimedia scene. A methodology for retrieval of wave parameters in regular wave conditions is also automatically handled by the software and will be discussed. In the context of performed measurements and achieved results, we will point out the extent to which consumer grade camera can fulfil automation and accuracy demands of industrial applications and the pitfalls entailed. Lastly, we will elaborate on visual representation of computed motion and deformations.
Directory of Open Access Journals (Sweden)
José Fermi Guerrero-Castellanos
2015-08-01
Full Text Available The present paper deals with the development of bounded feedback control laws mimicking the strategy adopted by flapping flyers to stabilize the attitude of systems falling within the framework of rigid bodies. Flapping flyers are able to orient their trajectory without any knowledge of their current attitude and without any attitude computation. They rely on the measurements of some sensitive organs: halteres, leg sensilla and magnetic sense, which give information about their angular velocity and the orientation of gravity and magnetic field vectors. Therefore, the proposed feedback laws are computed using direct inertial sensors measurements, that is vector observations with/without angular velocity measurements. Hence, the attitude is not explicitly required. This biomimetic approach is very simple, requires little computational power and is suitable for embedded applications on small control units. The boundedness of the control signal is taken into consideration through the design of the control laws by saturation of the actuators’ input. The asymptotic stability of the closed loop system is proven by Lyapunov analysis. Real-time experiments are carried out on a quadrotor using MEMS inertial sensors in order to emphasize the efficiency of this biomimetic strategy by showing the convergence of the body’s states in hovering mode, as well as the robustness with respect to external disturbances.
A heterogeneous system based on GPU and multi-core CPU for real-time fluid and rigid body simulation
da Silva Junior, José Ricardo; Gonzalez Clua, Esteban W.; Montenegro, Anselmo; Lage, Marcos; Dreux, Marcelo de Andrade; Joselli, Mark; Pagliosa, Paulo A.; Kuryla, Christine Lucille
2012-03-01
Computational fluid dynamics in simulation has become an important field not only for physics and engineering areas but also for simulation, computer graphics, virtual reality and even video game development. Many efficient models have been developed over the years, but when many contact interactions must be processed, most models present difficulties or cannot achieve real-time results when executed. The advent of parallel computing has enabled the development of many strategies for accelerating the simulations. Our work proposes a new system which uses some successful algorithms already proposed, as well as a data structure organisation based on a heterogeneous architecture using CPUs and GPUs, in order to process the simulation of the interaction of fluids and rigid bodies. This successfully results in a two-way interaction between them and their surrounding objects. As far as we know, this is the first work that presents a computational collaborative environment which makes use of two different paradigms of hardware architecture for this specific kind of problem. Since our method achieves real-time results, it is suitable for virtual reality, simulation and video game fluid simulation problems.
Wang, Yue; Xu, Shijie
2014-12-01
The motion of a rigid body in a uniformly rotating second degree and order gravity field is a good model for the gravitationally coupled orbit-attitude motion of a spacecraft in the close proximity of an asteroid. The relative equilibria of this full dynamics model are investigated using geometric mechanics from a global point of view. Two types of relative equilibria are found based on the equilibrium conditions: one is the Lagrangian relative equilibria, at which the circular orbit of the rigid body is in the equatorial plane of the central body; the other is the non-Lagrangian relative equilibria, at which the circular orbit is parallel to but not in the equatorial plane of central body. The existences of the Lagrangian and non-Lagrangian relative equilibria are discussed numerically with respect to the parameters of the gravity field and the rigid body. The effect of the gravitational orbit-attitude coupling is especially assessed. The existence region of the Lagrangian relative equilibria is given on the plane of the system parameters. Numerical results suggest that the negative C 20 with a small absolute value and a negative C 22 with a large absolute value favor the existence of the non-Lagrangian relative equilibria. The effect of the gravitational orbit-attitude coupling of the rigid body on the existence of the non-Lagrangian relative equilibria can be positive or negative, which depends on the harmonics C 20 and C 22, and the angular velocity of the rotation of the gravity field.
Efficient 3D rigid-body registration of micro-MR and micro-CT trabecular bone images
Rajapakse, C. S.; Magland, J.; Wehrli, S. L.; Zhang, X. H.; Liu, X. S.; Guo, X. E.; Wehrli, F. W.
2008-03-01
Registration of 3D images acquired from different imaging modalities such as micro-magnetic resonance imaging (ÂµMRI) and micro-computed tomography (ÂµCT) are of interest in a number of medical imaging applications. Most general-purpose multimodality registration algorithms tend to be computationally intensive and do not take advantage of the shape of the imaging volume. Multimodality trabecular bone (TB) images of cylindrical cores, for example, tend to be misaligned along and around the axial direction more than that around other directions. Additionally, TB images acquired by ÂµMRI can differ substantially from those acquired by ÂµCT due to apparent trabecular thickening from magnetic susceptibility boundary effects and non-linear intensity correspondence. However, they share very similar contrast characteristics since the images essentially represent a binary tomographic system. The directional misalignment and the fundamental similarities of the two types of images can be exploited to achieve fast 3D registration. Here we present an intensity cross-correlation based 3D registration algorithm for registering 3D specimen images from cylindrical cores of cadaveric TB acquired by ÂµMRI and ÂµCT in the context of finite-element modeling to assess the bone's mechanical constants. The algorithm achieves the desired registration by first coarsely approximating the three translational and three rotational parameters required to align the ÂµMR images to the ÂµCT scan coordinate frame and fine-tuning the parameters in the neighborhood of the approximate solution. The algorithm described here is suitable for 3D rigid-body image registration applications where through-plane rotations are known to be relatively small. The accuracy of the technique is constrained by the image resolution and in-plane angular increments used.
The Rigid Body Type Poisson Structure for the Constrained NLS System%约束的NLS系统的刚体型Poisson结构
Institute of Scientific and Technical Information of China (English)
杜殿楼; 马云苓
2005-01-01
A constrained system associated with a 3×3 matrix spectral problem of the nonlinear Schrodinger(NLS) hierarchy is proposed. It is shown that the constrained system is a Hamiltonian system with the rigid body type Poisson structure on the Poisson manifold R3N. Further, the reduction of the constrained system extended to the common level set of the complex cones is proved to be the constrained AKNS system on C2N.
Institute of Scientific and Technical Information of China (English)
Meng Wanli; Chen Renliang
2013-01-01
This paper focuses on the prediction of the safe autorotation landing operations of a helicopter following engine failure. The autorotation landing procedure is formulated as a nonlinear optimal control problem based on an augmented six-degree-of-freedom rigid-body flight dynamic model. First, the cost function and constraints are properly selected. The direct transcription approach is then employed to solve the optimal control problem. For a UH-60 helicopter, the opti-mal solutions with the rigid-body model are compared with those obtained using a two-dimensional point-mass model. It is found that the optimal solutions using the two different models show rea-sonably good agreement, and furthermore the optimal solutions using the rigid-body model involve the time histories of angular rates and attitudes, lateral velocity and position, as well as pitch con-trols. Finally the optimal control formulations with different cost functions are proposed for taking account of 1-s time delay and minimum touchdown speed. The calculated control strategies and trajectories are realistic.
Energy Technology Data Exchange (ETDEWEB)
Unseren, M.A.
1997-04-20
The paper reviews a method for modeling and controlling two serial link manipulators which mutually lift and transport a rigid body object in a three dimensional workspace. A new vector variable is introduced which parameterizes the internal contact force controlled degrees of freedom. A technique for dynamically distributing the payload between the manipulators is suggested which yields a family of solutions for the contact forces and torques the manipulators impart to the object. A set of rigid body kinematic constraints which restrict the values of the joint velocities of both manipulators is derived. A rigid body dynamical model for the closed chain system is first developed in the joint space. The model is obtained by generalizing the previous methods for deriving the model. The joint velocity and acceleration variables in the model are expressed in terms of independent pseudovariables. The pseudospace model is transformed to obtain reduced order equations of motion and a separate set of equations governing the internal components of the contact forces and torques. A theoretic control architecture is suggested which explicitly decouples the two sets of equations comprising the model. The controller enables the designer to develop independent, non-interacting control laws for the position control and internal force control of the system.
Elastic clearance change in axisymmetric shearing process
Yoshida, Yoshinori
2016-10-01
An axisymmetric shearing experiment is conducted for a sheet of low carbon steel and stainless steel. Elastic change in the clearance between punch and die is measured. The increase of the clearance in shearing is confirmed and the influence of sheared material's flow stress on the clearance change is shown. Finite element analysis (FEA) of shearing with Gurson-Tvergaard-Needlman model (GTN model) is conducted for shearing of the carbon steels with rigid tools as a numerical experiment. Burr height is predicted in the FEA and the result is compared with the experimental result. In addition, the influence of the clearance on stress state in the material is investigated.
Directory of Open Access Journals (Sweden)
Pål Johan From
2012-04-01
Full Text Available This paper presents the explicit dynamic equations of a mechanical system. The equations are presented so that they can easily be implemented in a simulation software or controller environment and are also well suited for system and controller analysis. The dynamics of a general mechanical system consisting of one or more rigid bodies can be derived from the Lagrangian. We can then use several well known properties of Lie groups to guarantee that these equations are well defined. This will, however, often lead to rather abstract formulation of the dynamic equations that cannot be implemented in a simulation software directly. In this paper we close this gap and show what the explicit dynamic equations look like. These equations can then be implemented directly in a simulation software and no background knowledge on Lie theory and differential geometry on the practitioner's side is required. This is the first of two papers on this topic. In this paper we derive the dynamics for single rigid bodies, while in the second part we study multibody systems. In addition to making the equations more accessible to practitioners, a motivation behind the papers is to correct a few errors commonly found in literature. For the first time, we show the detailed derivations and how to arrive at the correct set of equations. We also show through some simple examples that these correspond with the classical formulations found from Lagrange's equations. The dynamics is derived from the Boltzmann--Hamel equations of motion in terms of local position and velocity variables and the mapping to the corresponding quasi-velocities. Finally we present a new theorem which states that the Boltzmann--Hamel formulation of the dynamics is valid for all transformations with a Lie group topology. This has previously only been indicated through examples, but here we also present the formal proof. The main motivation of these papers is to allow practitioners not familiar with
Glukharev, K. K.; Morozova, N. I.; Potemkin, B. A.; Solovyev, V. S.; Frolov, K. V.
1973-01-01
A mathematical model of the human body was constructed, under the action of harmonic vibrations, in the 2.5-7 Hz frequency range. In this frequency range, the model of the human body as a vibrating system, with concentrated parameters is considered. Vertical movements of the seat and vertical components of vibrations of the human body are investigated.
Pathak, Ashish; Raessi, Mehdi
2016-04-01
We present a three-dimensional (3D) and fully Eulerian approach to capturing the interaction between two fluids and moving rigid structures by using the fictitious domain and volume-of-fluid (VOF) methods. The solid bodies can have arbitrarily complex geometry and can pierce the fluid-fluid interface, forming contact lines. The three-phase interfaces are resolved and reconstructed by using a VOF-based methodology. Then, a consistent scheme is employed for transporting mass and momentum, allowing for simulations of three-phase flows of large density ratios. The Eulerian approach significantly simplifies numerical resolution of the kinematics of rigid bodies of complex geometry and with six degrees of freedom. The fluid-structure interaction (FSI) is computed using the fictitious domain method. The methodology was developed in a message passing interface (MPI) parallel framework accelerated with graphics processing units (GPUs). The computationally intensive solution of the pressure Poisson equation is ported to GPUs, while the remaining calculations are performed on CPUs. The performance and accuracy of the methodology are assessed using an array of test cases, focusing individually on the flow solver and the FSI in surface-piercing configurations. Finally, an application of the proposed methodology in simulations of the ocean wave energy converters is presented.
Romano, Marcello
2012-01-01
The exact analytic solution is introduced for the rotational motion of a rigid body having three equal principal moments of inertia and subjected to an external torque vector which is constant for an observer fixed with the body, and to arbitrary initial angular velocity. In the paper a parametrization of the rotation by three complex numbers is used. In particular, the rows of the rotation matrix are seen as elements of the unit sphere and projected, by stereographic projection, onto points on the complex plane. In this representation, the kinematic differential equation reduces to an equation of Riccati type, which is solved through appropriate choices of substitutions, thereby yielding an analytic solution in terms of confluent hypergeometric functions. The rotation matrix is recovered from the three complex rotation variables by inverse stereographic map. The results of a numerical experiment confirming the exactness of the analytic solution are reported. The newly found analytic solution is valid for any...
Panciroli, Riccardo; Porfiri, Maurizio
2013-12-01
The objective of this work is to verify the accuracy of indirect pressure measurement from particle image velocimetry in water entry problems. The pressure is evaluated by solving the incompressible Navier-Stokes equations, whose kinematic components are estimated from particle image velocimetry. We focus on the water entry of a rigid wedge, for which we explore variations of the entry velocity. Experimental results are verified through comparison with well-established analytical formulations based on potential flow theory. Our findings demonstrate the feasibility of accurately reconstructing the hydrodynamic pressure field over the entire duration of the impact. Along with a thorough experimental validation of the method, we also offer insight into experimentally relevant factors, such as the maximum resolved fluid velocity and the required spatial integration area.
1976-10-01
transformation (R] 2 Society of Naval trchitects and Marine Engineers, " Nomenclature for Treating the Motion of a Submerged Body through a Fluid ," SNAKE Technical...of Naval Architects and Marine Engineers, " Nomenclature for Treating the Motion of a Submerged Body through a Fluid ," SNAME Technical and Research
Connolly, C. M.; Konik, A.; Dasari, P. K. R.; Segars, P.; Zheng, S.; Johnson, K. L.; Dey, J.; King, M. A.
2011-03-01
Patient motion can cause artifacts, which can lead to difficulty in interpretation. The purpose of this study is to create 3D digital anthropomorphic phantoms which model the location of the structures of the chest and upper abdomen of human volunteers undergoing a series of clinically relevant motions. The 3D anatomy is modeled using the XCAT phantom and based on MRI studies. The NURBS surfaces of the XCAT are interactively adapted to fit the MRI studies. A detailed XCAT phantom is first developed from an EKG triggered Navigator acquisition composed of sagittal slices with a 3 x 3 x 3 mm voxel dimension. Rigid body motion states are then acquired at breath-hold as sagittal slices partially covering the thorax, centered on the heart, with 9 mm gaps between them. For non-rigid body motion requiring greater sampling, modified Navigator sequences covering the entire thorax with 3 mm gaps between slices are obtained. The structures of the initial XCAT are then adapted to fit these different motion states. Simultaneous to MRI imaging the positions of multiple reflective markers on stretchy bands about the volunteer's chest and abdomen are optically tracked in 3D via stereo imaging. These phantoms with combined position tracking will be used to investigate both imaging-data-driven and motion-tracking strategies to estimate and correct for patient motion. Our initial application will be to cardiacperfusion SPECT imaging where the XCAT phantoms will be used to create patient activity and attenuation distributions for each volunteer with corresponding motion tracking data from the markers on the body-surface. Monte Carlo methods will then be used to simulate SPECT acquisitions, which will be used to evaluate various motion estimation and correction strategies.
Bertolesi, Elisa; Milani, Gabriele; Casolo, Siro
2016-12-01
A simple homogenized rigid body and spring model (HRBSM) is presented and applied for the non-linear dynamic analysis of 3D masonry structures. The approach, previously developed by the authors for the modeling of in-plane loaded walls is herein extended to real 3D buildings subjected to in- and out-of-plane deformation modes. The elementary cell is discretized by means of three-noded plane stress elements and non-linear interfaces. At a structural level, the non-linear analyses are performed replacing the homogenized orthotropic continuum with a rigid element and non-linear spring assemblage (RBSM) by means of which both in and out of plane mechanisms are allowed. All the simulations here presented are performed using the commercial software Abaqus. In order to validate the proposed model for the analyses of full scale structures subjected to seismic actions, two different examples are critically discussed, namely a church façade and an in-scale masonry building, both subjected to dynamic excitation. The results obtained are compared with experimental or numerical results available in literature.
Almesallmy, Mohammed
Methodologies are developed for dynamic analysis of mechanical systems with emphasis on inertial propulsion systems. This work adopted the Lagrangian methodology. Lagrangian methodology is the most efficient classical computational technique, which we call Equations of Motion Code (EOMC). The EOMC is applied to several simple dynamic mechanical systems for easier understanding of the method and to aid other investigators in developing equations of motion of any dynamic system. In addition, it is applied to a rigid multibody system, such as Thomson IPS [Thomson 1986]. Furthermore, a simple symbolic algorithm is developed using Maple software, which can be used to convert any nonlinear n-order ordinary differential equation (ODE) systems into 1st-order ODE system in ready format to be used in Matlab software. A side issue, but equally important, we have started corresponding with the U.S. Patent office to persuade them that patent applications, claiming gross linear motion based on inertial propulsion systems should be automatically rejected. The precedent is rejection of patent applications involving perpetual motion machines.
Hysteresis and the transition between axisymmetric flow and wave flow in the baroclinic annulus
Miller, Timothy L.; Butler, Karen A.
1991-01-01
A numerical model is employed to establish the transitions between axisymmetric flow and wave flow in the rotating, differentially heated annulus experiments of Fein for both rigid lid and free surface cases. It is shown that, for most of the transitions, the method of computing a steady axisymmetric flow and then testing its linear stability to wave disturbance results in good agreement with the experiments. Implications for the investigation of the dynamics of the earth's atmosphere are considered.
Axisymmetric multiwormholes revisited
Clément, Gérard
2015-01-01
The construction of stationary axisymmetric multiwormhole solutions to gravitating field theories admitting toroidal reductions to three-dimensional gravitating sigma models is reviewed. We show that, as in the multi-black hole case, strut singularities always appear in this construction, except for very special configurations with an odd number of centers. We also review the analytical continuation of the multicenter solution across the $n$ cuts associated with the wormhole mouths. The resulting Riemann manifold has $2^n$ sheets interconnected by $2^{n-1}n$ wormholes. We find that the maximally extended multicenter solution can never be asymptotically locally flat in all the Riemann sheets.
Energy Technology Data Exchange (ETDEWEB)
Lamare, F [INSERM, U650, Laboratoire du Traitement de l' Information Medicale (LaTIM), Brest, F-29200 (France); Carbayo, M J Ledesma [ETSI Telecomunicacion Universidad Politecnica de Madrid, Ciudad Universitaria s/n 28040, Madrid (Spain); Cresson, T [INSERM, U650, Laboratoire du Traitement de l' Information Medicale (LaTIM), Brest, F-29200 (France); Kontaxakis, G [ETSI Telecomunicacion Universidad Politecnica de Madrid, Ciudad Universitaria s/n 28040, Madrid (Spain); Santos, A [ETSI Telecomunicacion Universidad Politecnica de Madrid, Ciudad Universitaria s/n 28040, Madrid (Spain); Rest, C Cheze Le [INSERM, U650, Laboratoire du Traitement de l' Information Medicale (LaTIM), Brest, F-29200 (France); Reader, A J [School of Chemical Engineering and Analytical Science, University of Manchester, Manchester (United Kingdom); Visvikis, D [INSERM, U650, Laboratoire du Traitement de l' Information Medicale (LaTIM), Brest, F-29200 (France)
2007-09-07
Respiratory motion in emission tomography leads to reduced image quality. Developed correction methodology has been concentrating on the use of respiratory synchronized acquisitions leading to gated frames. Such frames, however, are of low signal-to-noise ratio as a result of containing reduced statistics. In this work, we describe the implementation of an elastic transformation within a list-mode-based reconstruction for the correction of respiratory motion over the thorax, allowing the use of all data available throughout a respiratory motion average acquisition. The developed algorithm was evaluated using datasets of the NCAT phantom generated at different points throughout the respiratory cycle. List-mode-data-based PET-simulated frames were subsequently produced by combining the NCAT datasets with Monte Carlo simulation. A non-rigid registration algorithm based on B-spline basis functions was employed to derive transformation parameters accounting for the respiratory motion using the NCAT dynamic CT images. The displacement matrices derived were subsequently applied during the image reconstruction of the original emission list mode data. Two different implementations for the incorporation of the elastic transformations within the one-pass list mode EM (OPL-EM) algorithm were developed and evaluated. The corrected images were compared with those produced using an affine transformation of list mode data prior to reconstruction, as well as with uncorrected respiratory motion average images. Results demonstrate that although both correction techniques considered lead to significant improvements in accounting for respiratory motion artefacts in the lung fields, the elastic-transformation-based correction leads to a more uniform improvement across the lungs for different lesion sizes and locations.
Wave focusing using symmetry matching in axisymmetric acoustic gradient index lenses
Romero-García, V.; Cebrecos, A.; Picó, R.; Sánchez-Morcillo, V. J.; Garcia-Raffi, L. M.; Sánchez-Pérez, J. V.
2013-12-01
The symmetry matching between the source and the lens results in fundamental interest for lensing applications. In this work, we have modeled an axisymmetric gradient index (GRIN) lens made of rigid toroidal scatterers embedded in air considering this symmetry matching with radially symmetric sources. The sound amplification obtained in the focal spot of the reported lens (8.24 dB experimentally) shows the efficiency of the axisymmetric lenses with respect to the previous Cartesian acoustic GRIN lenses. The axisymmetric design opens new possibilities in lensing applications in different branches of science and technology.
Institute of Scientific and Technical Information of China (English)
HE Yuanan; HE Zuoyong
2003-01-01
Reconstruction of the surface acoustic field of axisymmetric body with arbitrary boundary conditions using near-field acoustic data is studied. The method of numerical reconstruction based on orthonormalization function expansion (OFE) and boundary element integral (BEI) is presented which can overcome the singular integral problem in the boundary integral equations. By numerical examples, the precision of reconstruction for the non-conformal surface with the axisymmetric or non-axisymmetric vibrating on axisymmetric body is given.The results of the numerical simulation are shown that this kind of reconstruction method is available for engineering.
Chelnokov, Yu. N.
2013-01-01
The problem of reducing the body-attached coordinate system to the reference (programmed) coordinate system moving relative to the fixed coordinate system with a given instantaneous velocity screw along a given trajectory is considered in the kinematic statement. The biquaternion kinematic equations of motion of a rigid body in normalized and unnormalized finite displacement biquaternions are used as the mathematical model of motion, and the dual orthogonal projections of the instantaneous velocity screw of the body motion onto the body coordinate axes are used as the control. Various types of correction (stabilization), which are biquaternion analogs of position and integral corrections, are proposed. It is shown that the linear (obtained without linearization) and stationary biquaternion error equations that are invariant under any chosen programmed motion of the reference coordinate system can be obtained for the proposed types of correction and the use of unnormalized finite displacement biquaternions and four-dimensional dual controls allows one to construct globally regular control laws. The general solution of the error equation is constructed, and conditions for asymptotic stability of the programmed motion are obtained. The constructed theory of kinematic control of motion is used to solve inverse problems of robot-manipulator kinematics. The control problem under study is a generalization of the kinematic problem [1, 2] of reducing the body-attached coordinate system to the reference coordinate system rotating at a given (programmed) absolute angular velocity, and the presentedmethod for solving inverse problems of robotmanipulator kinematics is a development of the method proposed in [3-5].
采用移轴技术在SAP5程序实现刚体模态计算%Using the technology of moving the axle to compute the pattern of rigid body
Institute of Scientific and Technical Information of China (English)
施群德
2001-01-01
Elaborates how to use the technology of moving the axle to compute the pattern of rigid body,introduces this technology into the program SAP5 and realizes the calculation of the pattern of rigid body.%论述了如何采用移轴技术实现对刚体模态的计算，并将移轴求刚体模态的技术引入著名的SAP5程序中，实现了对刚体模态的计算。
Howarth, Samuel J
2014-01-01
The purpose of this study was to compare the spine flexion angle time histories computed with the 2 described techniques (dot product [DP] and a modified joint coordinate system [JCS] approaches) that used vector algebra and used skin-mounted markers to the spine flexion angles derived using local coordinate systems constructed from rigid bodies affixed to the pelvis and thorax during spine flexion movements. Discrepancies between the simplified marker setup and a criterion standard (CS) method for measuring spine kinematics were quantified. Sixteen participants performed full forward spine flexion. Three-dimensional kinematic data were obtained from markers affixed bilaterally over the greater trochanters, iliac crests, and 10th ribs. Time varying spine flexion angles were derived from the 3-, and 2-dimensional marker data using a DP and a modified JCS approach. Criterion standard spine kinematics were obtained from clusters of markers adhered to 2 rigid fins that were affixed over the pelvis and trunk. The DP and JCS methods were compared with the CS by computing root mean squared differences and correlations during the spine flexion trials. Descriptive measurements of missing kinematic data were also obtained. On average, root mean squared differences were 30.1% lower for the JCS method of deriving spine flexion angles. Correlations were also higher for the JCS method by 2.5%, compared with the DP method. The findings suggest that the adapted JCS method is superior to the DP method for deriving spine flexion angles. This is especially true when only 2-dimensional coordinate data are available. Copyright © 2014 National University of Health Sciences. Published by Elsevier Inc. All rights reserved.
Leuridan, Steven; Goossens, Quentin; Roosen, Jorg; Pastrav, Leonard; Denis, Kathleen; Mulier, Michiel; Desmet, Wim; Vander Sloten, Jos
2017-02-01
Accurate pre-clinical evaluation of the initial stability of new cementless hip stems using in vitro micromotion measurements is an important step in the design process to assess the new stem's potential. Several measuring systems, linear variable displacement transducer-based and other, require assuming bone or implant to be rigid to obtain micromotion values or to calculate derived quantities such as relative implant tilting. An alternative linear variable displacement transducer-based measuring system not requiring a rigid body assumption was developed in this study. The system combined advantages of local unidirectional and frame-and-bracket micromotion measuring concepts. The influence and possible errors that would be made by adopting a rigid body assumption were quantified. Furthermore, as the system allowed emulating local unidirectional and frame-and-bracket systems, the influence of adopting rigid body assumptions were also analyzed for both concepts. Synthetic and embalmed bone models were tested in combination with primary and revision implants. Single-legged stance phase loading was applied to the implant - bone constructs. Adopting a rigid body assumption resulted in an overestimation of mediolateral micromotion of up to 49.7μm at more distal measuring locations. Maximal average relative rotational motion was overestimated by 0.12° around the anteroposterior axis. Frontal and sagittal tilting calculations based on a unidirectional measuring concept underestimated the true tilting by an order of magnitude. Non-rigid behavior is a factor that should not be dismissed in micromotion stability evaluations of primary and revision femoral implants. Copyright © 2017 Elsevier Ltd. All rights reserved.
4自由度并联机构刚体动力学模型%Rigid-body Dynamic Model of a Four-DOF Parallel Mechanism
Institute of Scientific and Technical Information of China (English)
贾凯凯; 梅江平; 刘松涛; 田二勋
2016-01-01
Focused on a 4-DOF parallel mechanism with the spatial motion called SCARA (three dimensional translation and one-dimensional rotation), the establishment of its simplified dynamic model of rigid body is systematically researched to improve the accuracy to solve torque. Based on the kinematics analysis, the complete dynamic model of rigid body is established with the virtual work principle, and its accuracy is examined by ADAMS. To reduce the computational complexity, taking the structure and state of motion in every moving part of the mechanism into consideration, the simplified dynamic model of rigid body with single parameter is established. For the expected simplification, when the mechanism is moving along the standard trajectory, the average of maximum absolute torque difference between values solved from the complete dynamic model and the simplified dynamic model as optimization function are taken and the relation between the function and scale parameters is analyzed. Under the authentication of the analysis results, based on a set of given parameters, the optimal value is obtained by using the single objective optimization method. The validity of the method is verified through a set of image contrast compared with existed theories.%以一种具有空间SCARA运动(三维平动和一维转动)的四自由度并联机构为研究对象，系统研究其简化刚体动力学模型的创建方法，提高了力矩求解精度。在运动学分析的基础上，利用虚功原理，建立机构的完备刚体动力学模型，并利用ADAMS校验该模型的正确性。考虑机构各活动构件的结构和运动状态，建立机构的单变量简化刚体动力学模型，奠定了变量优化的模型基础。以机构沿标准轨迹运动时，将完备模型和简化模型计算所得的单轴驱动力矩差值的最大值的绝对值的平均值作为优化目标，分析各尺度参数对优化目标的影响规律，为简化模型的最优
Institute of Scientific and Technical Information of China (English)
Xu Zhang; Wen-Xian Li; Yi-Rong Cai
2015-01-01
Background:In China,tracheobronchial foreign body (TFB) aspiration,a major cause of emergency episode and accident death in children,remains a challenge for anesthetic management.Here,we share our experience and discuss the anesthetic consideration and management of patients with TFB aspiration.Methods:This was a single-institution retrospective study in children with an inhaled foreign body between 1991 and 2010 that focused on the complications following rigid bronchoscopy (RB).Data including the clinical characteristics of patients and TFB,anesthetic method,and postoperative severe complications were analyzed by different periods.Results:During the 20-year study period,the charts of 3149 patients who underwent RB for suspected inhaled TFB were reviewed.There were 2079 male and 1070 female patients (1.94:1).A nut (84％) was the most commonly inhaled object.The study revealed a 9％ (n =284) overall rate of severe postoperative complications related to severe hypoxemia,laryngeal edema,complete laryngospasm,pneumothorax,total segmental atelectasis,and death with incidences of 3.2％,0.9％,1.3％,0.3％,0.3％,and 0.1％,respectively.The rates of preoperative airway impairment,negative findings of TFB,and adverse postoperative events have been on the rise in the past 5 years.Conclusions:The survey results confirmed that hypoxemia remains the most common postoperative complication in different periods.Both controlled ventilation and spontaneous ventilation were effective during the RB extraction of the foreign body at our hospital in the modern technique period.An active respiratory symptom was commonly seen in the groups with negative findings.
Institute of Scientific and Technical Information of China (English)
邓锂强
2013-01-01
The designing experiment of “modification of the experimental instrument of the rigid body moment of inertia”is introduced .The experiment requires students to understand the principles of moment of inertia and rigid body dynamics ,modification of the experimental in-strument of the rigid body moment of inertia ,using the existing laboratory instruments ,and to put forward new experimental principle .It can correct moment of resistance .This experimental device is required in measuring rigid body moment of inertia .%介绍了设计性实验“刚体转动惯量实验仪的改装”。以转动惯量及刚体动力学原理为基础，利用实验室现有仪器，对刚体转动惯量实验仪进行改装，并提出新的实验原理，可以对阻力矩进行修正，并利用该实验装置测量刚体转动惯量。
Numerical Study on Fixed-Axis Rotation of Rigid Body under Variable Moment Inertia%变转动惯量刚体定轴转动的数值研究
Institute of Scientific and Technical Information of China (English)
唐军杰; 王爱军; 赵昆; 张鹏
2012-01-01
Given a model of variable moment inertia of rigid body,a numerical method with Matlab has been applied to study the fixed-axis rotation of rigid body under variable moment inertia and constant external torque. Because at the initial stage the changes in variable moment inertia are very small , the movement of rigid body is similar to that when moment inertia is constant. As the changes in moment inertia become greater,the angular velocity of rigid body changes periodically under the impact of elastic restoring forces.%给出一个变转动惯量刚体模型,用数值方法研究了在恒力矩作用下变转动惯量刚体的定轴转动问题.在开始阶段由于转动惯量变化很小,刚体运动与刚体转动惯量不变的情况相似,随着转动惯量变化增大,在弹性恢复力的作用下,刚体角速度呈周期性变化.
Response of axisymmetric separated flow to its spatially localized perturbation
Dovgal, A. V.; Zanin, B. Yu.; Sorokin, A. M.
2016-11-01
The flow past an axisymmetric body with laminar boundary-layer separation in a low-velocity air stream has been studied. The hot-wire technique was employed to identify the variation of velocity field induced by a local stationary perturbation of separation region at the stern of the experimental model. A large-scale influence upon the near-wall flow due to a cylinder roughness element provided on the model surface was observed. The obtained data substantiate the possibility of controlling the laminar boundary-layer separation on an axisymmetric body using a local external forcing.
Wagner, Richard D., Jr.
1959-01-01
In a recent article on hypersonic flow, Lees and Kubota suggested a modification of the local-expansion method to predict the surface pressures in the region of a nose-cylinder junction where Newtonian theory fails. The modification consists of matching the Newtonian pressure distribution and the Prandtl-Meyer relation at the point on the nose surface where both the pressure and the pressure gradient, predicted by these two solution, are equal. With this approximation, the pressure distribution can be predicted quite accurately up to the nose-cylinder junction for blunt-nosed bodies of continuous curvature, provided centrifugal-force effects are negligible. The purpose of this note is to facilitate the application of Lees' suggestion and to draw attention to some of its consequences.
Institute of Scientific and Technical Information of China (English)
胡常莉; 王国玉
2014-01-01
为了研究绕不同头型回转体的空穴发展特性，采用高速录像技术分别观察了绕平头和半锥角为45°的锥头回转体在不同空化数下的形态特征，应用粒子测速系统（PIV）测量了其速度、涡量及湍流脉动等分布情况。研究表明，相比于锥头回转体，同一空化数条件下，平头回转体的空穴最大尺度较大，且其随空化数的变化率亦较大；平头回转体空穴在发展的过程中表现为大尺度空泡团的融合、脱落及溃灭，表现较大的脉动，锥头回转体则为小尺度空穴的溃灭及再融合进而溃灭，空穴的脉动较小；空穴区域对应于低速高脉动区域；随着空化数的减小，速度分布趋于均匀，空穴内部流动脉动增强，高湍动能区域逐渐增大。%A high-speed video camera was used to observe the process of cavity development,flow characteristics and effects of headforms around two axisymmetric bodies with blunt and 45° half cone angle shaped headforms re-spectively,with the circumstances of different cavitation numbers. A particle image velocimetry(PIV)system was employed to measure the velocity,vorticity and turbulent energy fields. The results show that at a given cavitation number,the maximum scale of the cavity around the blunt body is significantly bigger than that of the cone-shaped body. And as the cavitation number decreases,the cavities of the blunt body develop faster as compared with the cone-shaped body. It has been found that the process of cavity development around the blunt body represents a number of large cavity vortexes conjunct with each other,then they shed and disappear together with obvious un-steady characters,while there is a small scale cavity behaving around the cone-shaped body. In addition,from the flow field it appears that in the cavity area the flow speed is low and the instability is pronounced meanwhile the ve-locity distributing trends uniformly. What′s more,with the
Institute of Scientific and Technical Information of China (English)
刘稳航; 余尚江; 杨源祯; 马骁; 徐世钊; 宁奥杰
2015-01-01
韧性剪切带是构造地质学研究的重要内容。传统研究韧性剪切带主要是野外露头解析和室内显微构造研究来综合判断剪切带的属性。近些年来，许多国内外学者对于剪切带中刚体(砾石、颗粒等)的研究，特别是使用模拟软件(如：Ansys、Matlab、Mathcad)试图恢复刚体的运动学轨迹，拓宽了学者们对于韧性剪切带中赋存刚体的研究思路。目前，对于刚体的模拟研究介绍甚少。基于此，本文对韧性剪切带中如何定量研究刚体的理论进行详细的介绍，并利用 Mathcad 编写程序恢复了刚体在给定条件下的运动学轨迹。%Ductile shear zone is an important subject in the research of tectonics.The traditional study of duc-tile shear zone focuses on discrimination of property of shear zone through analysis of outcrops in the field and indoor study of microstructure.In recent years scholars from China and abroad tended to study the rigid bodies in shear zone (gravel and grain)and they attempted to recover the kinematic trajectory of rigid bodies by using simulation software (Ansys,Matlab,Mathcad)while it also broadened the ideas of research on rigid bodies occurred in ductile shear zone.In light of the scarcity of introduction to simulation study on rigid body,this paper elaborated on theories of quantitative study on rigid body in ductile shear zone and recovered kinematic trajectory of rigid bodies under certain conditions by using Mathcad.
Energy Technology Data Exchange (ETDEWEB)
Inoue, Minoru; Yoshimura, Michio, E-mail: myossy@kuhp.kyoto-u.ac.jp; Sato, Sayaka; Nakamura, Mitsuhiro; Yamada, Masahiro; Hirata, Kimiko; Ogura, Masakazu; Hiraoka, Masahiro [Department of Radiation Oncology and Image-Applied Therapy, Kyoto University Graduate School of Medicine, Kyoto 606-8507 (Japan); Sasaki, Makoto; Fujimoto, Takahiro [Division of Clinical Radiology Service, Kyoto University Hospital, Kyoto 606-8507 (Japan)
2015-04-15
Purpose: To investigate image-registration errors when using fiducial markers with a manual method and the point-based rigid-body registration (PRBR) algorithm in accelerated partial breast irradiation (APBI) patients, with accompanying fiducial deviations. Methods: Twenty-two consecutive patients were enrolled in a prospective trial examining 10-fraction APBI. Titanium clips were implanted intraoperatively around the seroma in all patients. For image-registration, the positions of the clips in daily kV x-ray images were matched to those in the planning digitally reconstructed radiographs. Fiducial and gravity registration errors (FREs and GREs, respectively), representing resulting misalignments of the edge and center of the target, respectively, were compared between the manual and algorithm-based methods. Results: In total, 218 fractions were evaluated. Although the mean FRE/GRE values for the manual and algorithm-based methods were within 3 mm (2.3/1.7 and 1.3/0.4 mm, respectively), the percentages of fractions where FRE/GRE exceeded 3 mm using the manual and algorithm-based methods were 18.8%/7.3% and 0%/0%, respectively. Manual registration resulted in 18.6% of patients with fractions of FRE/GRE exceeding 5 mm. The patients with larger clip deviation had significantly more fractions showing large FRE/GRE using manual registration. Conclusions: For image-registration using fiducial markers in APBI, the manual registration results in more fractions with considerable registration error due to loss of fiducial objectivity resulting from their deviation. The authors recommend the PRBR algorithm as a safe and effective strategy for accurate, image-guided registration and PTV margin reduction.
Seginer, A
2011-08-01
Medical guidance systems often employ several data sources using different coordinate systems. In order to map positions from one coordinate system to the other, these guidance systems usually employ rigid-body point-based registration, using pairs of fiducial points: pairs which describe the same physical positions, but in different coordinate systems. The customary test for the quality of the registration is the fiducial registration error (FRE), which is the root-mean-square of the mismatch between the fiducials in each pair (after the registration). The FRE, however, does not give an answer to the question which is usually of interest, and that is the accuracy at a "target" point which is not part of the set of fiducial points. The statistics of the target registration error (TRE) have been studied before and approximate expressions were derived, but those expressions require as input the unknown true fiducial positions. In the present paper, it is proven that by replacing these unknowable true positions with the known measured positions in the expression for mean-square TRE, a higher order approximation is achieved. In other words, it is shown that more accurate estimates are obtained by using less accurate, but available, inputs. Furthermore, in previous approximations FRE and TRE were shown to be statistically independent, whereas here, due to the higher approximation level, it is shown that a slight dependence exists. Thus, the knowledge of FRE can in fact be employed to improve predictions of the TRE statistics. These results are supported by simulations and hold even for fiducial localization error (FLE) distributions with large standard deviations.
Classification of Stellar Orbits in Axisymmetric Galaxies
Li, Baile; Khan, Fazeel
2014-01-01
It is known that two supermassive black holes (SMBHs) cannot merge in a spherical galaxy within a Hubble time; an emerging picture is that galaxy geometry, rotation, and large potential perturbations may usher the SMBH binary through the critical three-body scattering phase and ultimately drive the SMBH to coalesce. We explore the orbital content within an N-body model of a mildly- flattened, non-rotating, SMBH-embedded elliptical galaxy. When used as the foundation for a study on the SMBH binary coalescence, the black holes bypassed the binary stalling often seen within spherical galaxies and merged on Gyr timescales (Khan et al. 2013). Using both frequency-mapping and angular momentum criteria, we identify a wealth of resonant orbits in the axisymmetric model, including saucers, that are absent from an otherwise identical spherical system and that can potentially interact with the binary. We quantified the set of orbits that could be scattered by the SMBH binary, and found that the axisymmetric model contai...
Institute of Scientific and Technical Information of China (English)
屈稳太; 应蓓华; 董凤莲
2014-01-01
Calculation of large rigid body pose and its high precision control was studied herein .Ai‐ming at the 6-DOF large rigid body pose alignment system ,a fast calculation approach to the pose and a high precision multi-axis coordinating control system was presented .Firstly ,mathematic models of large rigid body pose calculation were established respectively on a global frame which was found on the basic platform and a body-fixed frame system which was found on the center of the large rigid body .By detecting the initial positions and the final positions of four marks on the large rigid body ,the displacement increments of three coordinates of the four supports could be easily calculated .Then ,a compensation of synchronization error integration technology was proposed for the large rigid body pose alignment system .By the technology ,the precision and speed of large rigid pose alignment could be improved significantly .The simulation results show that the proposed approach is rapid and effec‐tive ,the control algorithm has guiding significance for engineering applications of large rigid body pose alignment .%大刚体的姿态计算及其高精度控制是飞机、舰船等大型机器总装生产线的关键技术。针对一种六自由度的大刚体的姿态控制系统提出一种快速的姿态计算方法和高精度的多轴协调控制方法。以基础平台建立固定坐标系，以大刚体的中心建立连体坐标系，在此基础上建立大刚体姿态计算数学模型，通过测量大刚体上4个靶标的初始位置和目标位置，就可计算出大刚体4个支撑柱的三坐标的位移增量；在多轴同步控制技术中，引入同步误差积分补偿方法（CSEI），通过同步误差在相反方向的控制作用，可显著提高大刚体姿态调整的速度和精度。仿真表明，所提出的姿态计算方法和 CSEI 控制方法快速有效，对工程应用具有指导意义。
Acoustic Bessel-like beam formation by an axisymmetric grating
Jiménez, N.; Romero-García, V.; Picó, R.; Cebrecos, A.; Sánchez-Morcillo, V. J.; Garcia-Raffi, L. M.; Sánchez-Pérez, J. V.; Staliunas, K.
2014-04-01
We report Bessel-like beam formation of acoustic waves by means of an axisymmetric grating of rigid tori. The results show that the generated beam pattern is similar to that of Bessel beams, characterized by elongated non-diffracting focal spots. A multiple foci structure is observed, due to the finite size of the lens. The dependence of the focal distance on the frequency is also discussed, on the basis of an extended grating theory. Experimental validation of acoustic Bessel-like beam formation is also reported for sound waves. The results can be generalized to wave beams of different nature, as optical or matter waves.
2R Pseudo-Rigid-Body Dynamic Model of Compliant Mechanism With Moment Load%力矩载荷下的柔顺机构2R伪刚体动力学模型
Institute of Scientific and Technical Information of China (English)
李茜; 余跃庆
2011-01-01
Much research has been done in the structures and kinematics of compliant mechanisms based on the pseudo-rigid-body model. However, the study on the dynamics of compliant mechanisms is very little. In this paper, a new dynamic model of the compliant beam with moment load is proposed in terms of the 2R pseudo-rigid-body model. Then the dynamic equation of the compliant beam is derived by Lagrange equation,and the dynamic characteristic is analyzed with the proposed dynamic model. The characteristic curves are drown and discussed. Compared with the 1R pseudo-rigid-body model, the dynamic model of 2R pseudo-rigid-body can reflect the complicated deibrmation and motion of the compliant mechanisms exactly.%柔顺机构的研究在结构学及运动学方面取得了大量成果,但是在动力学方面的成果却很少.本文首次以柔顺杆为研究对象,建立其在力矩载荷下的2R伪刚体动力学模型,并应用拉格朗日方程推导出动力学方程,进行了动力学响应分析,给出了相应的动态位形图.同时与1R伪刚体动力学模型做比较,从方程、响应曲线等方面分析2R伪刚体动力学模型的特点,表明此模型的优越性.
Energy Technology Data Exchange (ETDEWEB)
Unseren, M.A.
1997-09-01
The report reviews a method for modeling and controlling two serial link manipulators which mutually lift and transport a rigid body object in a three dimensional workspace. A new vector variable is introduced which parameterizes the internal contact force controlled degrees of freedom. A technique for dynamically distributing the payload between the manipulators is suggested which yields a family of solutions for the contact forces and torques the manipulators impart to the object. A set of rigid body kinematic constraints which restricts the values of the joint velocities of both manipulators is derived. A rigid body dynamical model for the closed chain system is first developed in the joint space. The model is obtained by generalizing the previous methods for deriving the model. The joint velocity and acceleration variables in the model are expressed in terms of independent pseudovariables. The pseudospace model is transformed to obtain reduced order equations of motion and a separate set of equations governing the internal components of the contact forces and torques. A theoretic control architecture is suggested which explicitly decouples the two sets of equations comprising the model. The controller enables the designer to develop independent, non-interacting control laws for the position control and internal force control of the system.
Institute of Scientific and Technical Information of China (English)
杨永; 张根宝; 宁小磊; 陈连华
2011-01-01
In order to get rid of the limitation of Rodrigues parameter represents rigid body attitude, similar Rodrigues parameters were proposed for attitude determination in this paper, which would avoid singularity that appeared in Rodrigues parameters and modified Rodrigues parameters at π- π, 2π, -2π in definition. A simple derivation of similar Rodrigues parameters based attitude kinematics equation was presented. Coordinate transformation using similar Rodrigues parameters was given. The property and operation of similar Rodrigues parameters were discussed. The exclusion of attitude representation based on similar Rodrigues parameters was proved. The relationship of similar Rodrigues parameters with other attitude representation, such as Euler angle, quaternion, rotation vector and direction cosine matrix were also provided. A recursive solution of similar Rodrigues parameters was given to attitude algorithm to facilitate its application in SINS. The simulation results of some standard ballistic tracer which generated from STK in Matlab software showed that the attitude estimation algorithm using similar Rodrigues parameter could avoid the occurrence of singularity and was more efficient on calculations than widely used quaternion based kinematics equation, which was an important significance in theory and reference.%针对Rodrigues参数描述刚体姿态运动时的缺陷，提出了一种类Rodrigues参数的姿态估计算法，从定义上避免了Rodrigues参数和修正Rodrigues参数在π-，-π，2π，-2π时的奇异。推导了类Rodrigues参数描述的姿态运动学微分方程，给出了坐标变换的类Rodrigues参数描述，讨论了类Rodrigues的性质和运算，证明了类Rodrigues参数描述姿态的唯一性，并导出了类Rodrigues参数与其他常用姿态描述间的转换公式。给出了用于捷联惯导的姿态解算中的类Rodrigues递推解法。在Matlab软件中时基于STK生成的某标准弹道轨迹的仿真结果
Energy Technology Data Exchange (ETDEWEB)
Rykov, A I; Shmakov, A N; Kriventsov, V N [Siberian Synchrotron Radiation Center, Budker INP, Lavrentieva 11, Novosibirsk 630090 (Russian Federation); Ueda, Y; Isobe, M [Institute for Solid State Physics, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581 (Japan); Nakayama, N [Department of Advanced Materials Science and Engineering, Yamaguchi University, Ube 755-8611 (Japan); Pavlyukhin, Yu T; Petrov, S A [Institute of Solid State Chemistry MC, Siberian Branch RAS, Novosibirsk 630128 (Russian Federation); Vasiliev, A N, E-mail: rykov@woody.ocn.ne.j [Low Temperature Physics Department, Moscow State University, Moscow 119991 (Russian Federation)
2010-04-15
Rietveld profiles, Moessbauer spectra and x-ray absorption fine structure (XAFS) were used to analyze the source of the structural phase transition at T{sub s}=355 K in HoBaCo{sub 4}O{sub 7}. Excess of oxygen content over 'O{sub 7}' was avoided by annealing the samples in an argon flow at 600 {sup 0}C. Space groups (S.G.) Pbn2{sub 1} and P6{sub 3}mc were used to refine the structure parameters in the low- and high-temperature phases, respectively. Additionally, the Cmc2{sub 1} symmetry was considered as a concurrent model of structure of the low-temperature phase. In the high-temperature phase, severe anisotropy of thermal motion of the majority of the oxygen atoms was observed. The variation of quadrupole splitting {epsilon} near T{sub s} is not similar to the step-like anomaly frequently seen at the charge-ordering transition. We observe instead a dip-like anomaly of the average {epsilon} near T{sub s}. Narrow distribution of the electric field gradient (EFG) over different cobalt sites is observed. XAFS spectra show no evidence of significant difference between YBaCo{sub 4}O{sub 7} (T>T{sub s}) and HoBaCo{sub 4}O{sub 7} (T
Axisymmetric buckling of laminated thick annular spherical cap
Dumir, P. C.; Dube, G. P.; Mallick, A.
2005-03-01
Axisymmetric buckling analysis is presented for moderately thick laminated shallow annular spherical cap under transverse load. Buckling under central ring load and uniformly distributed transverse load, applied statically or as a step function load is considered. The central circular opening is either free or plugged by a rigid central mass or reinforced by a rigid ring. Annular spherical caps have been analysed for clamped and simple supports with movable and immovable inplane edge conditions. The governing equations of the Marguerre-type, first order shear deformation shallow shell theory (FSDT), formulated in terms of transverse deflection w, the rotation ψ of the normal to the midsurface and the stress function Φ, are solved by the orthogonal point collocation method. Typical numerical results for static and dynamic buckling loads for FSDT are compared with the classical lamination theory and the dependence of the effect of the shear deformation on the thickness parameter for various boundary conditions is investigated.
含刚性体可展开结构的展开过程动力学分析方法%Dynamic analysis of deployable structures with rigid bodies
Institute of Scientific and Technical Information of China (English)
吴明儿; 项平
2011-01-01
在可展结构中设置刚性体可以有效提高展开效率，保证形状精度，因此含刚性体可展结构具有较高的实用价值。刚性体按需要可为刚性曲板等，一般形状复杂且形式多样，含任意形状刚性体可展结构的展开过程动力学分析比较困难。本文以笛卡尔坐标系下节点坐标及位移为变量，利用广义逆矩阵建立了一种通用的刚性体动力学方程，给出了利用Newmark—β法进行展开过程动力学分析的数值计算方法。通过算例分析及与ADAMS软件结果进行对比，验证了本文方法的正确性。与传统的多体系统动力学方法相比，该分析方法的优点是数学描述简洁明快，包含的未知量少，能够有效地分析含任意形状刚性体的可展开结构动力学问题。%Deployable structures with internal rigid bodies can improve both the deploying efficiency and the deploying precision. Thus, this kind of hybrid deployable structures is of high practical value. The surface of rigid bodies can be curved panels or other shapes. There is no efficient method to analyze the deploying dynamic process of this kind of deployable structure by now because it is difficult to describe the rigid surface in analysis. In this paper, the dynamic equation of rigid body using nodal coordinates and displacements as variables was established at first. Then, the dynamic equation was introduced to the deploying process analysis through using Moore-Penrose generalized inverse matrix method and Newmark numerical integration. In the end, a numerical example was given and the validity of the method was investigated compared with the calculation results of soft package ADAMS. Compared with multi-body system dynamics,the method suggested in this paper is easy in formulation and can be used to analyze the dynamic problems of deployable structures consisting of rigid bodies with arbitrary shapes.
21 CFR 874.4710 - Esophagoscope (flexible or rigid) and accessories.
2010-04-01
... generic type of device includes the flexible foreign body claw, flexible biopsy forceps, rigid biopsy curette, flexible biopsy brush, rigid biopsy forceps and flexible biopsy curette, but excludes...
Gortler, Steven J; Liu, Ligang; Thurston, Dylan P
2010-01-01
We study the properties of affine rigidity of a hypergraph and prove a variety of fundamental results. First, we show that affine rigidity is a generic property (i.e., depends only on the hypergraph, not the particular embedding). Then we prove that a graph is generically neighborhood affinely rigid in d-dimensional space if it is (d+1)-vertex-connected. We also show neighborhood affine rigidity of a graph implies universal rigidity of its squared graph. Our results, and affine rigidity more generally, have natural applications in point registration and localization, as well as connections to manifold learning.
Directory of Open Access Journals (Sweden)
Steven J. Gortler
2013-12-01
Full Text Available We study the properties of affine rigidity of a hypergraph and prove a variety of fundamental results. First, we show that affine rigidity is a generic property (i.e., depends only on the hypergraph, not the particular embedding. Then we prove that a graph is generically neighborhood affinely rigid in d-dimensional space if it is (d+1-vertex-connected. We also show neighborhood affine rigidity of a graph implies universal rigidity of its squared graph. Our results, and affine rigidity more generally, have natural applications in point registration and localization, as well as connections to manifold learning.
Farghaly, S. H.; El-Sayed, T. A.
2017-01-01
The purpose of this article is to investigate the changes in the magnitude of natural frequencies and their associated modal shapes of Timoshenko beam with respect to different system design parameters. This beam includes an intermediate extended eccentric rigid mass mounted on two elastic segments. The equilibrium equations which govern the transverse and rotational motions are derived. The application of the developed system frequency equation is demonstrated by several illustrative examples. Several end and intermediate conditions are considered. The influence of, rotary inertia, shear deformation, axial load, eccentric mass and elastic segments step ratio on the system natural frequencies and mode shapes are conducted. Several sets of new results are presented. Comparison of the present model results with the experimental data for shaft integrated with intermediate rigid mass demonstrates the accuracy of the analysis in practical applications. The present model is valid for several industrial applications, such as mechanical, structural, naval and for wider range of applications.
Modeling and simulation for non-smooth dynamics of planar-motion rigid-body%非光滑平面运动刚体动力学建模与数值计算方法
Institute of Scientific and Technical Information of China (English)
王晓军; 杨小斌; 刘志军
2015-01-01
基于接触力学理论和线性互补问题的算法,给出了一种含接触、碰撞以及Coulomb干摩擦的平面运动刚体动力学的建模与数值计算方法. 文中的摩擦力模型采用Coulomb干摩擦模型;考虑刚体模型在接触点的局部变形,用局部变形量与变形速度的非线性函数表示物体间的法向接触力;应用牛顿欧拉方法建立系统的动力学方程. 为计算非光滑动力学方程,建立了摩擦定律的互补条件和互补关系式,并利用事件驱动法,将接触点黏滞与滑移运动状态切换的判断以及静摩擦力的计算转化成线性互补问题的求解. 最后通过数值算例分析含摩擦与碰撞平面运动刚体的动力学特性,并验证了该算法的有效性.%A modeling and numerical method for the dynamics of a planar motion rigid -body with contact , im-pact and Coulomb's dry friction is presented based on the theory of contact mechanics and the arithmetic of linear complementarity problem ( LCP) .The friction law adopts Coulomb's dry friction model .The local deformations in contact bodies are taken into account although bodies are assumed to be rigid .The normal contact forces are ex-pressed as nonlinear functions of penetration depth and its speed .The dynamical equatuons of the rigid -body are obtained by using Newton -Euler nethod .The complementarity conditions and formulations about the friction law are given in order to compute the non -smooth dynamical equatiions .Based on the event -driven scheme , the problems of detecting stick -slip state transitions and solving the static frictional forces are formulated and solved as a linear complementarity problem .Finally, the numerical example of a planar -motion rigid-body is given to analyze its dynamical behaviour affected by impact and dry friction as well as shown that the proposed method is effective .
6自由度在刚体初始轨迹中的数值研究%A Rigid Body Numerical Simulation Based on Six Degrees of Freedom Method
Institute of Scientific and Technical Information of China (English)
杨磊; 肖天航
2014-01-01
采用6自由度方法对刚体的运动姿态进行了仿真研究，通过求解刚体的动力学方程和运动学方程确定刚体的质心位置。在分析研究传统求解刚体欧拉角缺点的基础上，采用全角度转换的四元数法求解欧拉角，解决了非全角度转换的四元数法在大攻角情况下转换不准确的问题。对6自由度方法进行了算例验证，结果表明该方法正确、实用，与已有的模型相比具有更好的工程应用价值。%It introduces the simulation of rigid body motion attitude with six degrees of freedom method .In order to determine the CG position of the rigid body , it solves the equation of rigid body dynamics and kinematics e-quations .Based on the shortcomings analysis of traditional methods and comparing with non -point conversion quaternion method , it shows that the proposed method can avoid the problem of inaccurate conversion for solving speed and angle of attack .The results prove that this method is correct and practical , and has better value in en-gineering applications than the existing other methods .
A dynamo model for axisymmetric and non-axisymmetric solar magnetic fields
Jiang, J
2007-01-01
Increasing observations are becoming available about a relatively weak, but persistent, non-axisymmetric magnetic field co-existing with the dominant axisymmetric field on the Sun. It indicates that the non-axisymmetric magnetic field plays an important role in the origin of solar activity. A linear non-axisymmetric alpha2-Omega dynamo model is set up to discuss the characteristics of the axisymmetric m=0 and the first non-axisymmetric m=1 modes and to provide further the theoretical bases to explain the active longitude, flip-flop and other non-axisymmetric phenomena. The model consists of a updated solar internal differential rotation, a turbulent diffusivity varied with depth and an alpha-effect working at the tachocline in rotating spherical systems. The difference between the alpha2-Omega and the alpha-Omega models and the conditions to favor the non-axisymmetric modes with the solar-like parameters are also presented.
Institute of Scientific and Technical Information of China (English)
贺少华; 谢最伟; 吴新跃
2011-01-01
A new method was proposed for shock response modeling and computing for a planar multi-rigid-flexible body system by integrating the transfer matrix technique with its flexibility and higher computational efficiency.Adopting Newmark-β algorithm to linearize higher order terms in dynamic equations and modal shapes to express flexible body deformation, extended transfer matrixes of general rigid-bodies and special rigid bodies ( rigid homogeneous rectangular plate, rectangular sheet plate with elastic supports), general flexible-bodies and special flexible bodies ( Euler-Bernouui beam) in systems under base-transferred shock were established.The shock excitations included both translational and rotational components.Numerical iterative algorithm program based on Newmark-β method was also given.With an engineering example, the accuracy of this proposed method was verified by finite element method.The results show that the contribution of the rotational components of shock to the overall response can not be ignored.Although the objective of this study was a planar multi-rigid-flexible system, the proposed method could easily be extended to three-dimensional cases.%结合传递矩阵方法建模灵活和计算效率高的优点,提出了一种基于"传递矩阵"概念的多体系统冲击响应建模和计算方法.以受基础冲击的平面多刚柔系统为研究对象,采用Newmark-β法对元件的方程高阶项进行线性化,用模态方法处理柔体的变形,建立了一般刚体和典型刚体(刚性均质矩形板、带弹性支撑的刚性均质矩形薄板)、一般柔体和典型柔体(Euler-Bernouni梁)的冲击扩展传递矩阵,冲击激励包含平动和转动两种成分,给出了基于Newmark-β法的系统响应数值迭代求解算法程序.用一个工程实例,通过与有限元方法的对比,验证了方法的准确性,得出了转动冲击激励成分对总体响应的贡献不能忽略的结论.方法的研究对象虽然只是平面多
Zhou, S.-S.; Gao, X.-L.; He, Q.-C.
2011-02-01
A unified treatment of axisymmetric adhesive contact problems is provided using the harmonic potential function method for axisymmetric elasticity problems advanced by Green, Keer, Barber and others. The harmonic function adopted in the current analysis is the one that was introduced by Jin et al. (2008) to solve an external crack problem. It is demonstrated that the harmonic potential function method offers a simpler and more consistent way to treat non-adhesive and adhesive contact problems. By using this method and the principle of superposition, a general solution is derived for the adhesive contact problem involving an axisymmetric rigid punch of arbitrary shape and an adhesive interaction force distribution of any profile. This solution provides analytical expressions for all non-zero displacement and stress components on the contact surface, unlike existing ones. In addition, the newly derived solution is able to link existing solutions/models for axisymmetric non-adhesive and adhesive contact problems and to reveal the connections and differences among these solutions/models individually obtained using different methods at various times. Specifically, it is shown that Sneddon's solution for the axisymmetric punch problem, Boussinesq's solution for the flat-ended cylindrical punch problem, the Hertz solution for the spherical punch problem, the JKR model, the DMT model, the M-D model, and the M-D- n model can all be explicitly recovered by the current general solution.
AXISYMMETRIC FLOW THROUGH A PERMEABLE NEAR-SPHERE
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
An analytical approach is described for the axisymmetric flow through a permeable near-sphere with a modification to boundary conditions in order to account permeability. The Stokes equation was solved by a regular perturbation technique up to the second order correction in epsilon representing the deviation from the radius of nondeformed sphere. The drag and the flow rate were calculated and the results were evaluated from the point of geometry and the permeability of the surface. An attempt also was made to apply the theory to the filter feeding problem. The filter appendages of small ecologically important aquatic organisms were modeled as axisymmetric permeable bodies, therefore a rough model for this problem was considered here as an oblate spheroid or near-sphere.
Axisymmetric equilibria of a gravitating plasma with incompressible flows
Throumoulopoulos, G N
2001-01-01
It is found that the ideal magnetohydrodynamic equilibrium of an axisymmetric gravitating magnetically confined plasma with incompressible flows is governed by a second-order elliptic differential equation for the poloidal magnetic flux function containing five flux functions coupled with a Poisson equation for the gravitation potential, and an algebraic relation for the pressure. This set of equations is amenable to analytic solutions. As an application, the magnetic-dipole static axisymmetric equilibria with vanishing poloidal plasma currents derived recently by Krasheninnikov, Catto, and Hazeltine [Phys. Rev. Lett. {\\bf 82}, 2689 (1999)] are extended to plasmas with finite poloidal currents, subject to gravitating forces from a massive body (a star or black hole) and inertial forces due to incompressible sheared flows. Explicit solutions are obtained in two regimes: (a) in the low-energy regime $\\beta_0\\approx \\gamma_0\\approx \\delta_0 \\approx\\epsilon_0\\ll 1$, where $\\beta_0$, $\\gamma_0$, $\\delta_0$, and $\\...
Numerical experiments on the oscillations of a rotating, axisymmetric galaxy
Miller, R. H.; Vandervoort, Peter O.; Welty, Daniel E.; Smith, B. F.
1989-01-01
Modes of oscillation in six rotating, axisymmetric N-body systems are studied in a sequence of self-consistent, three-dimensional numerical experiments. The experimental systems are realizations of theoretical models of galaxies which are stellar-dynamical counterparts of uniformly rotating polytropes of index equal to 0.5. The ratio of the rotational kinetic energy to the gravitational potential energy ranges from 0.13 to 0.20. The systems oscillate axisymmetrically; the oscillations are interpreted as superpositions of a mode of radial pulsation and a Kelvin-like mode of oscillation. The experimental frequencies of these modes agree very well with theoretical predictions. When these modes are suppressed, the states of the experimental systems are very steady. The systems are dynamically unstable with respect to a toroidal mode when the ratio of the rotational kinetic energy to the gravitational potential energy exceeds a value lying between 0.16 and 0.17.
Numerical experiments on the oscillations of a rotating, axisymmetric galaxy
Energy Technology Data Exchange (ETDEWEB)
Miller, R.H.; Vandervoort, P.O.; Welty, D.E.; Smith, B.F. (Chicago Univ., IL (USA); NASA, Ames Research Center, Moffett Field, CA (USA))
1989-07-01
Modes of oscillation in six rotating, axisymmetric N-body systems are studied in a sequence of self-consistent, three-dimensional numerical experiments. The experimental systems are realizations of theoretical models of galaxies which are stellar-dynamical counterparts of uniformly rotating polytropes of index equal to 0.5. The ratio of the rotational kinetic energy to the gravitational potential energy ranges from 0.13 to 0.20. The systems oscillate axisymmetrically; the oscillations are interpreted as superpositions of a mode of radial pulsation and a Kelvin-like mode of oscillation. The experimental frequencies of these modes agree very well with theoretical predictions. When these modes are suppressed, the states of the experimental systems are very steady. The systems are dynamically unstable with respect to a toroidal mode when the ratio of the rotational kinetic energy to the gravitational potential energy exceeds a value lying between 0.16 and 0.17. 19 refs.
Generic Rigidity Matroids with Dilworth Truncations
Tanigawa, Shin-ichi
2010-01-01
We prove that the linear matroid that defines generic rigidity of $d$-dimensional body-rod-bar frameworks (i.e., structures consisting of disjoint bodies and rods mutually linked by bars) can be obtained from the union of ${d+1 \\choose 2}$ graphic matroids by applying variants of Dilworth truncation $n_r$ times, where $n_r$ denotes the number of rods. This leads to an alternative proof of Tay's combinatorial characterizations of generic rigidity of rod-bar frameworks and that of identified body-hinge frameworks.
某型转管机枪刚柔耦合多体发射动力学仿真%Simulation of Coupled Rigid and Flexible Multi-body Dynamics on Gatling Gun
Institute of Scientific and Technical Information of China (English)
李涛; 王瑞林; 张军挪; 蔡伟
2013-01-01
以某型转管机枪为对象,研究了将CAD软件中复杂实体模型导入到ADAMS软件中的方法；考虑转管机枪实际射击条件下土壤本构关系和射手边界问题,建立了驻锄—土壤参数模型与人—枪参数模型；以多刚体动力学和柔性多体动力学理论为基础,采用ADAMS/Flex柔性体模块,建立了某型转管机枪刚柔耦合的虚拟样机仿真模型.通过对所建立的模型构件之间添加相互作用力,并进行多体发射动力学仿真和分析,获得了自动机运动过程中各主要部件的动力学特性.选取机枪自动机的速度和位移为校验指标,通过与试验数据中枪口响应位移比较,证明建立的刚柔耦合模型科学合理、准确有效,为该枪后期的结构优化与改进提供了模拟试验平台.%The method of translation complex model from CAD to ADAMS was studied on the object of Gatling gun; considering the soil constitutive relationship and the striker boundary problem in the actual shooting condition,spade-soil system and Parameter models of man-gun system were built; based on rigid multi-body dynamics and flexible body dynamics theories,the coupled rigid and flexible ADAMS model of the Gatling gun was established by using ADAMS/Flex module.The whole gun's kinematics circumstances and a series of dynamic curves were obtained during the course of simulation and analysis of coupled rigid and flexible multi-body dynamics.The Model was testified rational,accuracy and effective by comparing simulating results with the experimental data of the velocity and displacement of muzzle,which has laid the foundation for further simulation and structural optimization.
Streamline topology of axisymmetric flows
DEFF Research Database (Denmark)
Brøns, Morten
Topological fluid mechanics in the sense of the present paper is the study and classification of flow patterns close to a critical point. Here we discuss the topology of steady viscous incompressible axisymmetric flows in the vicinity of the axis. Following previous studies the velocity field $v......$ is expanded in a Taylor series at a point on the axis, and the expansion coefficients are considered as bifurcation parameters. After a normal form transformation we easily obtain the most common bifurcations of the flow patterns. The use of non-linear normal forms provide a gross simplification, which...... to the authors knowledge has not been used systematically to high orders in topological fluid mechanics. We compare the general results with experimental and computational results on the Vogel-Ronneberg flow. We show that the topology changes observed when recirculating bubbles on the vortex axis are created...
Clark, Timothy B P
2011-01-01
In this paper we investigate the class of rigid monomial ideals. We give a characterization of the minimal free resolutions of certain classes of these ideals. Specifically, we show that the ideals in a particular subclass of rigid monomial ideals are lattice-linear and thus their minimal resolution can be constructed as a poset resolution. We then use this result to give a description of the minimal free resolution of a larger class of rigid monomial ideals by using $\\mathcal{L}(n)$, the lattice of all lcm-lattices of monomial ideals with $n$ generators. By fixing a stratum in $\\mathcal{L}(n)$ where all ideals have the same total Betti numbers we show that rigidity is a property which is upward closed in $\\mathcal{L}(n)$. Furthermore, the minimal resolution of all rigid ideals contained in a fixed stratum is shown to be isomorphic to the constructed minimal resolution.
Institute of Scientific and Technical Information of China (English)
罗宏
2014-01-01
Two pendulums were designed to demonstrate the translational motion and plane-paral-lel motion of rigid bodies .The periods of the two pendulums were deduced with Lagrange equation . The reason of the different periods of two pendulums was analyzed by comparing the Lagrange fuc-tio n .%设计了2种摆来分别演示刚体的平动和平面平行运动，并比较了在2种不同运动形式下摆的周期。用拉格朗日方程得到了两摆周期的表达式，通过比较二者的拉格朗日函数，分析了两摆周期不同的原因。
Johansson, Adam; Balter, James; Cao, Yue
2017-06-15
Respiratory motion can affect pharmacokinetic perfusion parameters quantified from liver dynamic contrast-enhanced MRI. Image registration can be used to align dynamic images after reconstruction. However, intra-image motion blur remains after alignment and can alter the shape of contrast-agent uptake curves. We introduce a method to correct for inter- and intra-image motion during image reconstruction. Sixteen liver dynamic contrast-enhanced MRI examinations of nine subjects were performed using a golden-angle stack-of-stars sequence. For each examination, an image time series with high temporal resolution but severe streak artifacts was reconstructed. Images were aligned using region-limited rigid image registration within a region of interest covering the liver. The transformations resulting from alignment were used to correct raw data for motion by modulating and rotating acquired lines in k-space. The corrected data were then reconstructed using view sharing. Portal-venous input functions extracted from motion-corrected images had significantly greater peak signal enhancements (mean increase: 16%, t-test, P < 0.001) than those from images aligned using image registration after reconstruction. In addition, portal-venous perfusion maps estimated from motion-corrected images showed fewer artifacts close to the edge of the liver. Motion-corrected image reconstruction restores uptake curves distorted by motion. Motion correction also reduces motion artifacts in estimated perfusion parameter maps. Magn Reson Med, 2017. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.
Institute of Scientific and Technical Information of China (English)
侯健; 张方方
2012-01-01
为研究非标准条件下高速旋转弹丸的刚体外弹道性能,基于坐标变换理论建立了地球曲率影响下的外弹道数学模型,分析了自然风对弹丸气动力及气动力矩的作用,并在考虑气温气压及重力加速度变化的基础上得到了非标准务件下旋转弹丸的刚体外弹道模型.利用该模型对某105 mm榴弹外弹道进行仿真,结果表明:地球曲率引起旋转弹丸外弹道性能参数值少量增加,且增加量随弹丸射程的增大而增加,验证了自然风对弹丸动态稳定性有较大影响,进而影响弹丸的各弹道参数的结论.%To study the rigid body external trajectory performance of spinning projectile under non-standard conditions,the effect of natural wind on earth curvature was analyzed. Moreover,a rigid body external trajectory model was established according to the variations in atmospheric pressure,temperature and acceleration of gravity. The simulation was carried out on the external trajectory of a 105 mm shrapnel by this model. The calculated results show that the external trajectory performance parameters are increased with the fire range by earth curvature,thereby verifying the influence of natural wind upon the dynamical stability of the projectile,which further affects the external trajectory performance parameters.
Kitada, Ryo; Sadato, Norihiro; Lederman, Susan J
2012-01-01
Rigid surfaces consisting of spatially jittered 2-D raised-dot patterns with different inter-element spacings were moved back and forth across the skin at three different speeds (10-fold range). Within each psychophysical experiment, participants numerically estimated the perceived magnitude of either unpleasantness (nonpainful) or roughness of 2-D raised-dot surfaces applied to two stationary body sites (experiment 1: fingers; experiment 2: forearm). The psychophysical functions for the two types of perceptual judgment were highly similar at both body loci; more specifically, the perceived magnitude of unpleasantness and roughness both increased monotonically as a power function of increasing inter-element spacing, with the rate of growth declining at the upper end of the continuum. These results suggest that inter-element spacing is a critical determinant of the perceived magnitude of unpleasantness (nonpainful), as well as of roughness. Each perceptual judgment also increased as a function of increasing relative speed at both body loci. However, the magnitude of this effect was significantly greater for perceived unpleasantness than for perceived roughness; conversely, the speed effect was significantly greater on the forearm than on the fingers. Several possible explanations for these findings are considered.
HOMOLOGY RIGIDITY OF GRASSMANNIANS
Institute of Scientific and Technical Information of China (English)
Li Fang; Duan Haibao
2009-01-01
Applying the theory of GrSbner basis to the Schubert presentation for the cohomology of Grassmannians [2], we extend the homology rigidity results known for the classical Grassmaniaas to the exceptional cases.
Diffusive dynamics and stochastic models of turbulent axisymmetric wakes
Rigas, G; Brackston, R D; Morrison, J F
2015-01-01
A modelling methodology to reproduce the experimental measurements of a turbulent flow under the presence of symmetry is presented. The flow is a three-dimensional wake generated by an axisymmetric body. We show that the dynamics of the turbulent wake- flow can be assimilated by a nonlinear two-dimensional Langevin equation, the deterministic part of which accounts for the broken symmetries which occur at the laminar and transitional regimes at low Reynolds numbers and the stochastic part of which accounts for the turbulent fluctuations. Comparison between theoretical and experimental results allows the extraction of the model parameters.
Theory of axisymmetric pendular rings.
Rubinstein, Boris Y; Fel, Leonid G
2014-03-01
We present the theory of liquid bridges between two solids, sphere and plane, with prescribed contact angles. We give explicit expressions for curvature, volume and surface area of pendular ring as functions of the filling angle ψ for all available types of menisci: catenoid, sphere, cylinder, nodoid and unduloid (the meridional profile of the latter may have inflection points). There exists a rich set of solutions of the Young-Laplace equation for the shape of an axisymmetric meniscus of constant mean curvature. In case when the solids do not contact each other, these solutions extend Plateau's sequence of meniscus evolution observed with increase of the liquid volume to include the unduloids at small filling angle, unduloids with multiple inflection points and multiple catenoids. The Young-Laplace equation with boundary conditions can be viewed as a nonlinear eigenvalue problem. Its unduloid solutions, menisci shapes and curvatures H(n)(s)(ψ), exhibit a discrete spectrum and are enumerated by two indices: the number n of inflection points on the meniscus meridional profile M and the convexity index s=±1 determined by the shape of a segment of M contacting the solid sphere: the shape is either convex, s=1, or concave, s=-1. For the fixed contact angles the set of the functions H(n)(s)(ψ) behaves in such a way that in the plane {ψ,H} there exists a bounded domain where H(n)(s)(ψ) do not exist for any distance between solids. The curves H(n)(s)(ψ) may be tangent to the boundary of domain which is a smooth closed curve. This topological representation allows to classify possible curves and introduce a saddle point notion. We observe several types of saddle points, and give their classification.
Institute of Scientific and Technical Information of China (English)
丁皓江; 徐荣桥; 国凤林
1999-01-01
Based on three-dimensional elastic equations for piezoelectric materials, the state equations for piezoelectric circular plate under axisymmetric deformation are derived. Applying Hankel transform to them and letting the free boundary terms resulting from Hankel transform be zero, a set of ordinary differential equations with constant coefficients and associated boundary conditions are obtained. Furthermore, two exact solutions corresponding to generalized rigid slipping and generalized elastic simple support are deduced. Then, the governing equations obtained reduce to equations for axisymmetric problem of transversely isotropic circular plate. Under the two types of boundary conditions of elastic simple support and rigid slipping, exact solutions are derived. Finally, numerical results are presented and applicability of the classical plate theory is discussed.
Weiss, Asia; Whiteley, Walter
2014-01-01
This book contains recent contributions to the fields of rigidity and symmetry with two primary focuses: to present the mathematically rigorous treatment of rigidity of structures, and to explore the interaction of geometry, algebra, and combinatorics. Overall, the book shows how researchers from diverse backgrounds explore connections among the various discrete structures with symmetry as the unifying theme. Contributions present recent trends and advances in discrete geometry, particularly in the theory of polytopes. The rapid development of abstract polytope theory has resulted in a rich theory featuring an attractive interplay of methods and tools from discrete geometry, group theory, classical geometry, hyperbolic geometry and topology. The volume will also be a valuable source as an introduction to the ideas of both combinatorial and geometric rigidity theory and its applications, incorporating the surprising impact of symmetry. It will appeal to students at both the advanced undergraduate and gradu...
Pal, Tanmoy; Bhattacharjee, Somendra M.
2016-05-01
The temperature dependence of DNA flexibility is studied in the presence of stretching and unzipping forces. Two classes of models are considered. In one case the origin of elasticity is entropic due to the polymeric correlations, and in the other the double-stranded DNA is taken to have an intrinsic rigidity for bending. In both cases single strands are completely flexible. The change in the elastic constant for the flexible case due to thermally generated bubbles is obtained exactly. For the case of intrinsic rigidity, the elastic constant is found to be proportional to the square root of the bubble number fluctuation.
DEFF Research Database (Denmark)
Troiano, Giovanni Maria
Deformable and shape-changing interfaces are rapidly emerging in the field of human-computer interaction (HCI). Deformable interfaces provide users with newer input possibilities such as bending, squeezing, or stretching, which were impossible to achieve with rigid interfaces. Shape-changing inte......Deformable and shape-changing interfaces are rapidly emerging in the field of human-computer interaction (HCI). Deformable interfaces provide users with newer input possibilities such as bending, squeezing, or stretching, which were impossible to achieve with rigid interfaces. Shape...
Aerodynamics characteristic of axisymmetric surface protuberance in supersonic regime
Qamar, Adnan
2012-01-01
The present work deals with the problem of an axi-symmetric surface protuberance mounted on a spherical nosed body of revolution. The numerical computations are carried out for laminar supersonic viscous flow for trapezoidal shape axi-symmetric protuberances. A free stream Mach number ranging from 3 to 8 in steps of 1 at a fixed free stream Reynolds number of 1.8x10(4) has been used in the present study. The steady solutions are obtained using a time marching approach. A newly developed Particle Velocity Upwinding (PVU) scheme has been used for the computation. The spatial flow pattern exhibits a strong bow shock in front of the hemispherical nose, which engulfs the entire base body. Near the protuberance, the fluid particle decelerates due to the adverse pressure created by the protuberance and thus the flow separates in front of the protuberance. This point of separation is found to be a function of Mach number and the protuberance shape. A low-pressure expansion region dominates the base region of the obstacle. The reattachment point for the base separation is also a function of Mach number. As the Mach number is increased the reattachment point shifts toward the protuberances base. A weak recompression shock is also seen in the base, which affects the separated zone behind the protuberance. The important design parameters such as skin friction, heat transfer, drag, and surface pressure coefficients are reported extensively.
Institute of Scientific and Technical Information of China (English)
冯金地
2016-01-01
通过猜想加证明的方式得到了求解刚体定轴转动惯量的一个新推论，由这个推论可以将组合定理进行推广。工程力学上常常遇到的求解形状复杂的均匀刚体的转动惯量时此推论将会特别有用。本文最后通过一道例题，说明它具有简单、快捷的优点，并有独到之处。%We obtain a new conclusion about solution of moment of inertia about a fixed axis by guess and proof in this article ,from the conclusion the com bination theorem of moment of inertia is generalized .It will be specially useful when we frequently confront solving moment of inertia of some com plicated - shaped rigid body on engineering mechanics .In the end we solve a problem for example by this conclusion to show its advantage of simpleness ,convenience and speciality .
Institute of Scientific and Technical Information of China (English)
田延岭; 郑欢莹; 周明岳; 任治
2012-01-01
The paper presented the analysis of a compliant guide mechanism used in micro/nano positioning stage based on the pseudo-rigid body(PRB) dynamics model.In order to examine the PRB dynamics characteristics of the compliant guide mechanism in the micro/nano positioning stage,the finite element analysis was also conducted.The computational analyses verified that the PRB model method of the mechanism dynamics analysis is feasible and effective.%本文以伪刚体(PRB)动力学模型为基础,对微纳米定位平台中的柔顺导向机构进行了分析.有限元分析的应用验证了柔顺导向机构在微纳米定位平台中伪刚体的动态特性.计算分析证明伪刚体模型法用于研究微纳米定位平台结构的动力学分析的可行性和有效性.
Boundary element method for internal axisymmetric flow
Directory of Open Access Journals (Sweden)
Gokhman Alexander
1999-01-01
Full Text Available We present an accurate fast method for the computation of potential internal axisymmetric flow based on the boundary element technique. We prove that the computed velocity field asymptotically satisfies reasonable boundary conditions at infinity for various types of inlet/exit. Computation of internal axisymmetric potential flow is an essential ingredient in the three-dimensional problem of computation of velocity fields in turbomachines. We include the results of a practical application of the method to the computation of flow in turbomachines of Kaplan and Francis types.
Stationary axisymmetric black holes with matter
Chodosh, Otis
2015-01-01
We provide a geometric framework for the construction of non-vacuum black holes whose metrics are stationary and axisymmetric. Under suitable assumptions we show that the Einstein equations reduce to an Einstein-harmonic map type system and analyze the compatibility of the resulting equations. This framework will be fundamental to our forthcoming construction of metric-stationary axisymmetric bifurcations of Kerr solving the Einstein--Klein--Gordon system, and as such, we include specializations of all of our formulas to the case of a time-periodic massive scalar field.
Institute of Scientific and Technical Information of China (English)
王毅; 宋卫东; 佟德飞
2014-01-01
固定鸭舵式二维弹道修正弹修正组件相对弹体具有不同的滚转角速度，传统6D弹道模型不能有效描述弹丸的运动特性和规律。针对该问题，在修正组件和弹体无气动耦合的假设下，研究了修正组件、弹体的运动与弹丸运动的关系，分析了弹丸飞行过程中两刚体间的相互作用，综合两刚体的运动学和动力学方程建立了7D弹道模型。针对某型尾翼稳定弹建立了仿真模型，并对不同面积、不同舵偏角、不同修正组件质量3种状态进行了仿真分析。仿真结果表明，该模型可有效描述弹丸在飞行过程中的运动状态，且能够反映弹丸的弹道特性和运动规律。该模型可用于该型弹丸的弹道解算，并为该类弹丸的研究提供依据。%The correction components of 2D trajectory correction projectile(TCP)with fixed-canard have different roll-angular velocities relative to the body,and 6D trajectory model can’t effectively describe the motion characteristics of the proj ectile.To solve this problem,the proj ectile was treated as two rigid bodies.Under the assumption that the front component and the aft component have no pneumatic coupling,new coordinate frames were built,and mathematical rela-tionship between the force of the fixed component and airflow by redefining attacking angle and side slip angle was described.The relations of the movement of proj ectile,the correction component and the body component were studied.The interactive force between two rigid bodies during flight was analyzed.The 7D ballistic model was built through integrating kinematic equations and dynamic equations.Aiming at one fin-stability shell,the simulation model was built,and the simulation was carried out.The results show that this model can describe the motion state in the flight and reflect the traj ectory characteristics.This model can be used for ballistic solution,and it provides reference for studying the proj
Numerical simulation of motion and deformation of ring bubble along body surface
Institute of Scientific and Technical Information of China (English)
倪宝玉; 张阿漫
2013-01-01
Numerical simulation for fluid flow over an attached rigid body with a deformable ring bubble is analyzed based on the velocity potential theory together with the boundary element method (BEM). The analysis is focused on the axisymmetric case. The bubble surface is treated as a well defined air-liquid interface and is tracked by a mixed Eulerian-Lagrangian method. The points of intersection between the bubble and body are treated, specially in the numerical procedure. The auxiliary function method is adopted to calculate the pressure on the body surface and in the flow field. The convergence study is undertaken to assess the developed numerical method and the computation code. Some case studies are undertaken in which the interactions between the bubble/body and the incoming flow field are simulated. The effects of various physical parameters on the interactions are investigated.
Energy Technology Data Exchange (ETDEWEB)
Meson, Alejandro M., E-mail: meson@iflysib.unlp.edu.ar; Vericat, Fernando, E-mail: vericat@iflysib.unlp.edu.ar [CONICET-UNLP, Instituto de Fisica de Liquidos y Sistemas Biologicos (IFLYSIB) (Argentina)
2011-12-15
We analyze when a multifractal spectrum can be used to recover the potential. This phenomenon is known as multifractal rigidity. We prove that for a certain class of potentials the multifractal spectrum of local entropies uniquely determines their equilibrium states. This leads to a classification which identifies two systems up to a change of variables.
Electrostatics of Rigid Polyelectrolytes
Energy Technology Data Exchange (ETDEWEB)
Wong, G.C.L.
2009-06-04
The organization of rigid biological polyelectrolytes by multivalent ions and macroions are important for many fundamental problems in biology and biomedicine, such as cytoskeletal regulation and antimicrobial sequestration in cystic fibrosis. These polyelectrolytes have been used as model systems for understanding electrostatics in complex fluids. Here, we review some recent results in theory, simulations, and experiments.
Electoral Stability and Rigidity
Levy, Michael Y
2016-01-01
Some argue that political stability is best served through a two-party system. This study refutes this. The author mathematically defines the stability and rigidity of electoral systems comprised of any quantity of electors and parties. In fact, stability is a function of the quantity of electors - i.e., the number of occupied seats at the table. As the number of electors increases, the properties of an electorate are increasingly well resolved, and well described by those of an electorate that is least excessive -- that is to say an electorate that is closest to equilibrium. Further, electoral rigidity is a function of the quantity of parties and their probabilities of representation. An absolutely rigid system admits no fluctuations -- whatever happens to one elector will happen to all electors. As the quantity of parties increases so does the number of party lines, and with it the quantity of alternatives with which to respond to an external stimulus. Rigidity is significant in a social system that places ...
Rigid body essential X-ray crystallography
DEFF Research Database (Denmark)
Bjerrum, Esben Jannik; Biggin, Philip C
2008-01-01
The ligand-binding domain (LBD) from the ionotropic glutamate receptor subtype 2 (GluR2) has been shown to adopt a range of ligand-dependent conformational states. These states have been described in terms of the rotation required to fit subdomain (lobe) 2 following superposition of subdomain (lo...
Obituary--rigid contact lenses.
Efron, Nathan
2010-10-01
Scleral and corneal rigid lenses represented 100 per cent of the contact lens market immediately prior to the invention of soft lenses in the mid-1960s. In the United Kingdom today, rigid lenses comprise 2 per cent of all new lens fits. Low rates of rigid lens fitting are also apparent in 27 other countries which have recently been surveyed. Thus, the 1998 prediction of the author that rigid lenses--also referred to as 'rigid gas permeable' (RGP) lenses or 'gas permeable' (GP) lenses--would be obsolete by the year 2010 has essentially turned out to be correct. In this obituary, the author offers 10 reasons for the demise of rigid lens fitting: initial rigid lens discomfort; intractable rigid lens-induced corneal and lid pathology; extensive soft lens advertising; superior soft lens fitting logistics; lack of rigid lens training opportunities; redundancy of the rigid lens 'problem solver' function; improved soft toric and bifocal/varifocal lenses; limited uptake of orthokeratology; lack of investment in rigid lenses; and the emergence of aberration control soft lenses. Rigid lenses are now being fitted by a minority of practitioners with specialist skills/training. Certainly, rigid lenses can no longer be considered as a mainstream form of contact lens correction. May their dear souls (bulk properties) rest in peace.
Interaction of two high Reynolds number axisymmetric turbulent wakes
Obligado, M.; Klein, S.; Vassilicos, J. C.
2015-11-01
With the recent discovery of non-equilibrium high Reynolds number scalings in the wake of axisymmetric plates (Nedic et al., PRL, 2013), it has become of importance to develop an experimental technique that permits to easily discriminate between different wake scalings. We propose an experimental setup that tests the presence of non-equilibrium turbulence using the streamwise variation of velocity fluctuations between two bluff bodies facing a flow. We have studied two different sets of plates (one with regular and another with irregular peripheries) with Hot-Wire Anemometry in a wind tunnel. By acquiring streamwise profiles for different plate separations and identifying the wake interaction length for each separation it is possible to estimate the streamwise evolution of the single wake width. From this evolution it is also possible to deduce the turbulence dissipation scalings. This work generalizes previous studies on the interaction of plane wakes (see Gomes-Fernandes et al., JFM, 2012) to include axisymmetric wakes. We find that the wake interaction length proposed in this cited work and a constant anisotropy assumption can be used to collapse the streamwise developments of the first three moments.
He, Chenxu; Wylie, William
2011-01-01
In this paper we study the space of solutions to an overdetermined linear system involving the Hessian of functions. We show that if the solution space has dimension greater than one, then the underlying manifold has a very rigid warped product structure. This warped product structure will be used to study warped product Einstein structures in our paper "The space of virtual solutions to the warped product Einstein equation".
Saye, Robert
2017-09-01
In this two-part paper, a high-order accurate implicit mesh discontinuous Galerkin (dG) framework is developed for fluid interface dynamics, facilitating precise computation of interfacial fluid flow in evolving geometries. The framework uses implicitly defined meshes-wherein a reference quadtree or octree grid is combined with an implicit representation of evolving interfaces and moving domain boundaries-and allows physically prescribed interfacial jump conditions to be imposed or captured with high-order accuracy. Part one discusses the design of the framework, including: (i) high-order quadrature for implicitly defined elements and faces; (ii) high-order accurate discretisation of scalar and vector-valued elliptic partial differential equations with interfacial jumps in ellipticity coefficient, leading to optimal-order accuracy in the maximum norm and discrete linear systems that are symmetric positive (semi)definite; (iii) the design of incompressible fluid flow projection operators, which except for the influence of small penalty parameters, are discretely idempotent; and (iv) the design of geometric multigrid methods for elliptic interface problems on implicitly defined meshes and their use as preconditioners for the conjugate gradient method. Also discussed is a variety of aspects relating to moving interfaces, including: (v) dG discretisations of the level set method on implicitly defined meshes; (vi) transferring state between evolving implicit meshes; (vii) preserving mesh topology to accurately compute temporal derivatives; (viii) high-order accurate reinitialisation of level set functions; and (ix) the integration of adaptive mesh refinement. In part two, several applications of the implicit mesh dG framework in two and three dimensions are presented, including examples of single phase flow in nontrivial geometry, surface tension-driven two phase flow with phase-dependent fluid density and viscosity, rigid body fluid-structure interaction, and free
Saye, Robert
2017-09-01
In this two-part paper, a high-order accurate implicit mesh discontinuous Galerkin (dG) framework is developed for fluid interface dynamics, facilitating precise computation of interfacial fluid flow in evolving geometries. The framework uses implicitly defined meshes-wherein a reference quadtree or octree grid is combined with an implicit representation of evolving interfaces and moving domain boundaries-and allows physically prescribed interfacial jump conditions to be imposed or captured with high-order accuracy. Part one discusses the design of the framework, including: (i) high-order quadrature for implicitly defined elements and faces; (ii) high-order accurate discretisation of scalar and vector-valued elliptic partial differential equations with interfacial jumps in ellipticity coefficient, leading to optimal-order accuracy in the maximum norm and discrete linear systems that are symmetric positive (semi)definite; (iii) the design of incompressible fluid flow projection operators, which except for the influence of small penalty parameters, are discretely idempotent; and (iv) the design of geometric multigrid methods for elliptic interface problems on implicitly defined meshes and their use as preconditioners for the conjugate gradient method. Also discussed is a variety of aspects relating to moving interfaces, including: (v) dG discretisations of the level set method on implicitly defined meshes; (vi) transferring state between evolving implicit meshes; (vii) preserving mesh topology to accurately compute temporal derivatives; (viii) high-order accurate reinitialisation of level set functions; and (ix) the integration of adaptive mesh refinement. In part two, several applications of the implicit mesh dG framework in two and three dimensions are presented, including examples of single phase flow in nontrivial geometry, surface tension-driven two phase flow with phase-dependent fluid density and viscosity, rigid body fluid-structure interaction, and free
Rigidly connected magnetic lines: twisting and winding of magnetic lines
Prasad, G.
2017-10-01
The dynamical process of magnetic flux variation in a fluid's stream tube is described by constructing 1+1+ (2) decomposition of the gradient of fluid's 4-velocity. The necessary and sufficient conditions are obtained for a spacelike congruence to be a congruence of rigidly connected spacelike curves. The evolution of magnetic flux in a magnetic tube is explored under the assumptions that magnetic lines are rigidly connected and the chemical potential of the fluid is constant along a magnetic tube. The interplay between magnetic and stream tubes is demonstrated. It is shown that the growth of magnetic energy in a magnetic tube cannot exceed to that of a stream tube. It is found that the proper time variation of twist of magnetic lines is caused by gravitation inside a neutron star if magnetic lines are rigidly connected and charge neutrality condition holds. Helmholtz-like magnetic vorticity flux conservation in a magnetic tube constituted by rigidly connected geodetic magnetic lines is derived under the assumption that the charge neutrality condition holds. It is shown that the winding of frozen-in poloidal magnetic field due to differential rotation requires meridional circulation in an axisymmetric stationary hydromagnetic configuration.
Non-rigid body static model based miniature robotic arm pose estimation%基于非刚体静力模型的微型机械臂姿态估计
Institute of Scientific and Technical Information of China (English)
雷洋; 田书林; 程玉华
2012-01-01
A model based estimation approach is proposed to determine the real-time kinematic pose of a miniature cable driven robotic arm with ten passive planar rotation joints. A non-rigid body static equilibrium model is constructed, and the ten planar degree of freedom ( DOF) variables are transformed to one translational variable and one tensile force variable. An linear variable differential transformer(LVDT) sensor and a load cell are used in this robotic arm to measure the planar kinematic pose of its end actuator. The accuracy and error of the measurement results are analyzed; the advantage and insufficiency of this measurement approach are stated; and the proposed method is compared with other potential measurement schemes.%提出了一种针对具有10个被动平面转动关节的微型化柔索驱动机械臂运动姿态的实时估计方法.通过建立该微型机械臂的非刚体静力模型,将10个平面自由度变量转化为1个位移变量和1个张力变量.用一个线型差动变压位移传感器(linear variable differential transformer,LVDT)和一个微型载荷传感器(load cell)测量该微型机械臂终端执行器的平面运动姿态.通过对测量结果的精度和误差进行分析,指出了该测量方法的优势与不足,并与其他几种可能的测量方法进行了比较和讨论.
Axisymmetric free vibrations of infinite micropolar thermoelastic plate
Institute of Scientific and Technical Information of China (English)
Rajneesh Kumar; Geeta Partap
2007-01-01
The propagation of axisymmetric free vibrations in an infinite homogeneous isotropic micropolar thermoelastic plate without energy dissipation subjected to stress free and rigidly fixed boundary conditions is investigated. The secular equations for homogeneous isotropic micropolar thermoelastic plate without energy dissipation in closed form for symmetric and skew symmetric wave modes of propagation are derived. The different regions of secular equations are obtained. At short wavelength limits, the secular equations for symmetric and skew symmetric modes of wave propagation in a stress free insulated and isothermal plate reduce to Rayleigh surface wave frequency equation.The results for thermoelastic, micropolar elastic and elastic materials are obtained as particular cases from the derived secular equations. The amplitudes of displacement components, microrotation and temperature distribution are also computed during the symmetric and skew symmetric motion of the plate. The dispersion curves for symmetric and skew symmetric modes and amplitudes of displacement components, microrotation and temperature distribution in case of fundamental symmetric and skew symmetric modes are presented graphically. The analytical and numerical results are found to be in close agreement.
Global stability analysis of axisymmetric boundary layers
Vinod, N
2016-01-01
This paper presents the linear global stability analysis of the incompressible axisymmetric boundary layer on a circular cylinder. The base flow is parallel to the axis of the cylinder at inlet. The pressure gradient is zero in the streamwise direction. The base flow velocity profile is fully non-parallel and non-similar in nature. The boundary layer grows continuously in the spatial directions. Linearized Navier-Stokes(LNS) equations are derived for the disturbance flow quantities in the cylindrical polar coordinates. The LNS equations along with homogeneous boundary conditions forms a generalized eigenvalues problem. Since the base flow is axisymmetric, the disturbances are periodic in azimuthal direction. Chebyshev spectral collocation method and Arnoldi's iterative algorithm is used for the solution of the general eigenvalues problem. The global temporal modes are computed for the range of Reynolds numbers and different azimuthal wave numbers. The largest imaginary part of the computed eigenmodes are nega...
An axisymmetric steady state vortex ring model
Wang, Ruo-Qian
2016-01-01
Based on the solution of Atanasiu et al. (2004), a theoretical model for axisymmetric vortex flows is derived in the present study by solving the vorticity transport equation for an inviscid, incompressible fluid in cylindrical coordinates. The model can describe a variety of axisymmetric flows with particular boundary conditions at a moderately high Reynolds number. This paper shows one example: a high Reynolds number laminar vortex ring. The model can represent a family of vortex rings by specifying the modulus function using a Rayleigh distribution function. The characteristics of this vortex ring family are illustrated by numerical methods. For verification, the model results compare well with the recent direct numerical simulations (DNS) in terms of the vorticity distribution and streamline patterns, cross-sectional areas of the vortex core and bubble, and radial vorticity distribution through the vortex center. Most importantly, the asymmetry and elliptical outline of the vorticity profile are well capt...
Clumps and Axisymmetric Features in Debris Discs
Jiang, Ing-Guey
2013-01-01
This paper studied the structures of debris discs, focusing on the conditions that can form an axisymmetric-looking outer disc from systems with inner clumps. The main conclusion was that as long as the dominated dust grains are smaller than the blowout size, it is easy to form an axisymmetric-looking outer debris disc, which is part of a quasi-steady state of the whole system. This quasi-steady state is established through the balance between grain generations and a continuous out-going grain flow. Assuming there is an event that starts planetesimal collisions and the corresponding grain generations, this balance can be approached in a few thousand years. This result suggested that a quasi-steady-state picture could solve the possible mass budget problem of Vega's outer debris disc.
Institute of Scientific and Technical Information of China (English)
S·M·阿布德尔-盖德; M·R·伊德
2011-01-01
在一个轴对称、外形任意的多孔介质二维体中,充满了有屈服应力的非Newton幂律流体时,数值分析其自由对流及其传热/传质问题,利用相似变换,将边界层控制方程及其边界条件变换为无量纲形式,然后用有限差分法求解该方程组.所研究的参数为流变常数、浮力比和Lewis数.给出并讨论了典型的速度、温度及浓度曲线,发现屈服应力参数值和非Newton流体的幂律指数对结果有着显著的影响.%Numerical analysis of free convection coupled heat and mass transfer was presented for non-Newtonian power-law fluids with yield stress flowing over two-dimensional or axisymmetric body of arbitrary shape in a fluid-saturated porous medium.The governing boundary layer equations and boundary conditions were cast into a dimensionless form by similarity transformation and the resulting system of equations was solved by a finite difference method.The parameters studied were the rheologicai constants, the buoyancy ratio, and the Lewis number.Representative velocity as well as temperature and concentration profiles were presented and discussed.It was found that the result depend strongly on the values of the yield stress parameter, and the power-law index of non-Newtonian fluid.
Numerical simulations of rotating axisymmetric sunspots
Botha, G. J. J.; Busse, F.H.; Hurlburt, N. E.; Rucklidge, A.M.
2008-01-01
A numerical model of axisymmetric convection in the presence of a vertical magnetic flux bundle and rotation about the axis is presented. The model contains a compressible plasma described by the nonlinear MHD equations, with density and temperature gradients simulating the upper layer of the sun's convection zone. The solutions exhibit a central magnetic flux tube in a cylindrical numerical domain, with convection cells forming collar flows around the tube. When the numerical domain is rotat...
Numerical simulations of rotating axisymmetric sunspots
Botha, Gert; Busse, F.H.; Hurlburt, Neal; Rucklidge, Alistair
2008-01-01
A numerical model of axisymmetric convection in the presence of a vertical magnetic flux bundle and rotation about the axis is presented. The model contains a compressible plasma described by the non-linear MHD equations, with density and temperature gradients simulating the upper layer of the Sun’s convection zone. The solutions exhibit a central magnetic flux tube in a cylindrical numerical domain, with convection cells forming collar flows around the tube. When the numerical domain is rota...
Exact axisymmetric Taylor states for shaped plasmas
Energy Technology Data Exchange (ETDEWEB)
Cerfon, Antoine J., E-mail: cerfon@cims.nyu.edu; O' Neil, Michael, E-mail: oneil@cims.nyu.edu [Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 (United States)
2014-06-15
We present a general construction for exact analytic Taylor states in axisymmetric toroidal geometries. In this construction, the Taylor equilibria are fully determined by specifying the aspect ratio, elongation, and triangularity of the desired plasma geometry. For equilibria with a magnetic X-point, the location of the X-point must also be specified. The flexibility and simplicity of these solutions make them useful for verifying the accuracy of numerical solvers and for theoretical studies of Taylor states in laboratory experiments.
Axisymmetric instability in a noncircular tokamak
Energy Technology Data Exchange (ETDEWEB)
Lipschultz, B.
1979-10-01
The stability of dee, inverse-dee and square cross section plasmas to axisymmetric modes has been investigated experimentally in Tokapole II, a tokamak with a four-null poloidal divertor. Experimental results are closely compared with predictions of two numerical stability codes - the PEST code (ideal MHD, linear stability) adapted to tokapole geometry and a code which follows the nonlinear evolution of shapes similar to tokapole equilibria.
Torsional Rigidity of Minimal Submanifolds
DEFF Research Database (Denmark)
Markvorsen, Steen; Palmer, Vicente
2006-01-01
We prove explicit upper bounds for the torsional rigidity of extrinsic domains of minimal submanifolds $P^m$ in ambient Riemannian manifolds $N^n$ with a pole $p$. The upper bounds are given in terms of the torsional rigidities of corresponding Schwarz symmetrizations of the domains in warped...... for the torsional rigidity are actually attained and give conditions under which the geometric average of the stochastic mean exit time for Brownian motion at infinity is finite....
Stability of the Shallow Axisymmetric Parabolic-Conic Bimetallic Shell by Nonlinear Theory
M. Jakomin; Kosel, F.
2011-01-01
In this contribution, we discuss the stress, deformation, and snap-through conditions of thin, axi-symmetric, shallow bimetallic shells of so-called parabolic-conic and plate-parabolic type shells loaded by thermal loading. According to the theory of the third order that takes into account the balance of forces on a deformed body, we present a model with a mathematical description of the system geometry, displacements, stress, and thermoelastic deformations. The equations are based on the lar...
Rigid collapsible dish structure
Palmer, William B. (Inventor); Giebler, Martin M. (Inventor)
1982-01-01
A collapsible dish structure composed of a plurality of rows of rigid radial petal assemblies concentric with the axis of the dish. The petal assemblies consist of a center petal and two side petals, the center petal hinged on an axis tangent to a circle concentric with the axis of the dish and the side petals hinged to the center petal at their mating edge. The center petal is foldable inwardly and the side petals rotate about their hinges such that the collapsed dish structure occupies a much smaller volume than the deployed dish. Means of controlling the shape of the dish to compensate for differential expansion of the deployed dish are also provided.
McGrath, Paul L
2014-01-01
In this thesis, I examine in detail the properties of rigid quasilocal frames (RQF), which have been proposed as a geometrically natural way to define spatially extended reference frames in general relativity. I also explore their usefulness, in particular, as a tool for constructing completely general conservation laws that do not rely on the presence of spacetime symmetries and include both matter and gravitational contributions without the need for any ad hoc structures such as pseudotensors. In doing so, I show how the RQF approach affords a deeper understanding of the nature of gravitational fluxes via the equivalence principle. Finally, I apply the RQF formalism to explore Ehrenfest's rotating disk paradox, a generalization of Archimedes' law to curved spacetime, tidal interactions for Earth's and Jupiter's moons, and more.
DEFF Research Database (Denmark)
Troiano, Giovanni Maria
to convey particular information (e.g., big-isurgent, loud-is-up). The second work presents a large-scale analysis of 340 Sci-Fi movies that identifies instances of shape-changing interfaces. Results from the analysis reveals emergent behavioral patterns of shape change, namely Reconfiguration......Deformable and shape-changing interfaces are rapidly emerging in the field of human-computer interaction (HCI). Deformable interfaces provide users with newer input possibilities such as bending, squeezing, or stretching, which were impossible to achieve with rigid interfaces. Shape......-changing interfaces can reconfigure their shape dynamically, providing users with new affordances and output modalities. This thesis contributes to both the field of deformable interfaces and shape-changing interfaces through empirical research. In the area of deformable interfaces, this thesis presents two studies...
Low Cost Method of Manufacturing Cooled Axisymmetric Scramjets Project
National Aeronautics and Space Administration — Scramjet engine developers are working on advanced axisymmetric engine concepts that may not be feasible due to limitations of currently available manufacturing...
Axisymmetric oscillations of magnetic neutron stars
Lee, Umin
2007-01-01
We calculate axisymmetric oscillations of rotating neutron stars composed of the surface fluid ocean, solid crust and fluid core, taking account of a dipole magnetic field as strong as BS ~ 1015 G at the surface. The adiabatic oscillation equations for the solid crust threaded by a dipole magnetic field are derived in Newtonian dynamics, on the assumption that the axis of rotation is aligned with the magnetic axis so that perturbations on the equilibrium can be represented by series expansions in terms of spherical harmonic functions Yml(θ, φ) with different degrees l for a given azimuthal wave number m around the magnetic axis. Although the three component models can support a rich variety of oscillation modes, axisymmetric (m = 0) toroidal ltn and spheroidal lsn shear waves propagating in the solid crust are our main concerns, where l and n denote the harmonic degree and the radial order of the modes, respectively. In the absence of rotation, axisymmetric spheroidal and toroidal modes are completely decoupled, and we consider the effects of rotation on the oscillation modes only in the limit of slow rotation. We find that the oscillation frequencies of the fundamental toroidal torsional modes ltn in the crust are hardly affected by the magnetic field as strong as BS ~ 1015 G at the surface. As the radial order n of the shear modes in the crust becomes higher, however, both spheroidal and toroidal modes become susceptible to the magnetic field, and their frequencies in general get higher with increasing BS. We also find that the surface g modes and the crust/ocean interfacial modes are suppressed by a strong magnetic field, and that there appear magnetic modes in the presence of a strong magnetic field.
Reversed straining in axisymmetric compression test
DEFF Research Database (Denmark)
Arentoft, Mogens; Wanheim, Tarras; Lindegren, Maria
2005-01-01
to simulate these conditions a reversed axisymmetrical material tester is designed and constructed. Three different materials were tested, aluminum alloy AA6082, technically pure copper (99.5%) and cold forging steel Ma8, at different temperatures found during cold forging.......A large group of the cold forging processes is carried out in a thick – walled container with the deformation force transmitted through a punch moving axially in the container. The work piece, being entrapped between punch and container will expand and exert a radial pressure resulting...
VERTICAL VIBRATION ANALYSIS OF AXISYMMETRIC SATURATED SOIL
Institute of Scientific and Technical Information of China (English)
CAI Yuan-qiang; XU Chang-jie; ZHENG Zao-feng; WU Da-zhi
2006-01-01
Based on Biot's dynamic consolidation equations, by means of Laplace-Hankel transform technology, the integral solutions of stress and displacement in saturated soil with subjacent rock-stratum under axisymmetric arbitrary excitations were derived. Influence of the reflected wave generated by the boundary was revealed. Numerical results indicate that the vibration frequency has some effect on the vertical displacement of saturated soil. The vertical displacement at the surface of saturated soil lags in phase with the load. Furthermore, the dynamic permeability coefficient of saturated soil has significant effect on the vertical displacement at the initial stage of load applied, but when the load becomes stable, the effect is inapparent.
Distribution of Topological Defects on Axisymmetric Surface
Institute of Scientific and Technical Information of China (English)
SI Tie-Yan; DUAN Yi-Shi
2006-01-01
We propose a general method of determining the distribution of topological defects on axisymmetric surface,and study the distribution of topological defects on biconcave-discoid surface, which is the geometric configuration of red blood cell. There are three most possible cases of the distribution of the topological defects on the biconcave surface:four defects charged with 1/2, two defects charged with +1, or one defect charged with 2. For the four defect charged with 1/2, they sit at the vertices of a square imbedded in the equator of biconcave surface.
International rigid contact lens prescribing.
Efron, Nathan; Morgan, Philip B; Helland, Magne; Itoi, Motozumi; Jones, Deborah; Nichols, Jason J; van der Worp, Eef; Woods, Craig A
2010-06-01
Rigid lenses have been fitted less since the introduction of soft lenses nearly 40 years ago. Data that we have gathered from annual contact lens fitting surveys conducted in Australia, Canada, Japan, the Netherlands, Norway, the UK and the USA between 2000 and 2008 facilitate an accurate characterization of the pattern of the decline of rigid lens fitting during the first decade of this century. There is a trend for rigid lenses to be utilized primarily for refitting those patients who are already successful rigid lens wearers-most typically older females being refit with higher Dk materials. Rigid lenses are generally fitted on a full-time basis (four or more days of wear per week) without a planned replacement schedule. Orthokeratology is especially popular in the Netherlands, but is seldom prescribed in the other countries surveyed.
Quantum charged rigid membrane
Energy Technology Data Exchange (ETDEWEB)
Cordero, Ruben [Departamento de Fisica, Escuela Superior de Fisica y Matematicas del I.P.N., Unidad Adolfo Lopez Mateos, Edificio 9, 07738 Mexico, D.F. (Mexico); Molgado, Alberto [Unidad Academica de Fisica, Universidad Autonoma de Zacatecas, Zacatecas Zac. (Mexico); Rojas, Efrain, E-mail: cordero@esfm.ipn.mx, E-mail: amolgado@fisica.uaz.edu.mx, E-mail: efrojas@uv.mx [Departamento de Fisica, Facultad de Fisica e Inteligencia Artificial, Universidad Veracruzana, 91000 Xalapa, Veracruz (Mexico)
2011-03-21
The early Dirac proposal to model the electron as a charged membrane is reviewed. A rigidity term, instead of the natural membrane tension, involving linearly the extrinsic curvature of the worldvolume swept out by the membrane is considered in the action modeling the bubble in the presence of an electromagnetic field. We set up this model as a genuine second-order derivative theory by considering a non-trivial boundary term which plays a relevant part in our formulation. The Lagrangian in question is linear in the bubble acceleration and by means of the Ostrogradski-Hamiltonian approach, we observed that the theory comprises the management of both first- and second-class constraints. We thus show that our second-order approach is robust allowing for a proper quantization. We found an effective quantum potential which permits us to compute bounded states for the system. We comment on the possibility of describing brane world universes by invoking this kind of second-order correction terms.
Quantum charged rigid membrane
Cordero, Ruben; Rojas, Efrain
2010-01-01
The early Dirac proposal to model the electron as a charged membrane is reviewed. A rigidity term, instead of the natural membrane tension, involving linearly the extrinsic curvature of the worldvolume swept out by the membrane is considered in the action modeling the bubble in the presence of an electromagnetic field. We set up this model as a genuine second-order derivative theory by considering a non-trivial boundary term which plays a relevant part in our formulation. The Lagrangian in question is linear in the bubble acceleration and by means of the Ostrogradski-Hamiltonian approach we observed that the theory comprises the management of both first- and second-class constraints. We show thus that our second-order approach is robust allowing for a proper quantization. We found an effective quantum potential which permits to compute bounded states for the system. We comment on the possibility of describing brane world universes by invoking this kind of second-order correction terms.
Axisymmetric fretting analysis in coated cylinder
Indian Academy of Sciences (India)
M Ramesh; Satish V Kailas; K R Y Simha
2008-06-01
Fretting is essentially a contact fatigue phenomenon, although bulk stresses and material properties contribute to ﬁnal failure. The near surface state of stress developed under oscillatory contact between machine elements plays a major role in deciding the severity of fretting. It is possible to enhance tribological properties by coating the surface. There is rather scanty literature available on fretting analysis of coated components. Presence of such coatings has a large inﬂuence on the near surface state of stress. The effect of coatings on the severity of fretting is the focus of this paper. Results obtained for both hard and soft coatings are compared with the results obtained for the homogeneous case. The component geometry and loading are chosen to be cylindrical to enable 3D elastic axisymmetric fretting analysis. The results are compared with 2D models (strip and half-plane) to examine their utility and validity for understanding axisymmetric fretting. Contact pressure and frictional shear loading cases are solved separately and superposed appropriately depending on the coefﬁcient of friction considered. Results for different values of coefﬁcient of friction and elastic mismatch are illustrated through contour plots of stresses and strains. These results are expected to be helpful for identifying fretting failure zones and fracture mechanisms in coated components. Analytical results presented here could serve as useful benchmarks for calibrating numerical codes and experimental techniques.
Linear lateral vibration of axisymmetric liquid briges
Ferrera, C.; Montanero, J. M.; Cabezas, M. G.
A liquid bridge is a mass of liquid sustained by the action of the surface tension force between two parallel supporting disks Apart from their basic scientific interest a liquid bridge can be considered as the simplest idealization of the configuration appearing in the floating zone technique used for crystal growth and purification of high melting point materials footnote Messeguer et al emph Crystal Growth Res bf 5 27 1999 This has conferred considerable interest on the study of liquid bridges not only in fluid mechanics but also in the field of material engineering The axisymmetric dynamics of an isothermal liquid bridge has been frequently analysed over the past years The studies have considered different phenomena such as free oscillations footnote Montanero emph E J Mech B Fluids bf 22 169 2003 footnote Acero and Montanero emph Phys Fluids bf 17 078105 2005 forced vibrations footnote Perales and Messeguer emph Phys Fluids A bf 4 1110 1992 g-jitter effects footnote Messeguer and Perales emph Phys Fluids A bf 3 2332 1991 extensional deformation footnote Zhang et al emph J Fluid Mech bf 329 207 1996 and breakup process footnote Espino et al emph Phys Fluids bf 14 3710 2002 among others Works considering the nonaxisymmetric dynamical behaviour of a liquid bridge has been far less common footnote Sanz and Diez emph J Fluid Mech bf 205 503 1989 In the present study the linear vibration of an axisymmetric liquid
Multi-component, rigidly rotating polytropes: improved and extended theory
Caimmi, R
2016-01-01
With respect to earlier investigations, the theory of multi-component, concentric, copolar, axisymmetric, rigidly rotating polytropes is improved and extended, including subsystems with nonzero density on the boundary and subsystems with intersecting boundaries. The formulation is restricted to two subsystems for simplicity but, in principle, can be extended to $N$ subsystems. Equilibrium configurations are independent of the nature of the fluid i.e. collisional or collisionless, provided the polytropic index lies within the range, $1/2\\le n\\le5$, as in one-component systems. The solution of the equilibrium equations is expanded in power series, which can be continued up to the boundary and outside via starting points placed at increasingly larger distance from the centre of mass. A detailed analysis is devoted to special cases where the solution of the equilibrium equations can be expressed analytically. Finally a guidance example is shown, involving homogeneous subsystems with intersecting boundaries, where...
COHERENT STRUCTURES IN COUNTERCURRENT AXISYMMETRIC SHEAR FLOWS
Institute of Scientific and Technical Information of China (English)
谢锡麟; 麻伟巍; 周慧良
2003-01-01
The dynamical behaviors of coherent structures in countercurrent axisymmetric shear flows are experimentally studied. The forward velocity U1 and the velocity ratio R = (U1 - U2)/(U1 +U2), where U2 denotes the suction velocity, are considered as the control parameters. Two kinds of vortex structures, i.e., axisymmetric and helical structures, were discovered with respect to different regimes in the R versus U1 diagram. In the case of U1 ranging from 3 to 20 m/s and R from 1 to 3, the axisymmetric structures play an important role. Based on the dynamical behaviors of axisymmetric structures, a critical forward velocity Ucr1 = 6.8 m/s was defined, subsequently, the subcritical velocity regime: U1 ＞ Ucr1 and the supercritical velocity regime: U1 ＜ Ucr1. In the subcritical velocity regime,the flow system contains shear layer self-excited oscillations in a certain range of the velocity ratio with respect to any forward velocity. In the supercritical velocity regime, the effect of the velocity ratio could be explained by the relative movement and the spatial evolution of the axisymmetric structure undergoes the following stages: (1) Kelvin-Helmholtz instability leading to vortex rolling up, (2) first time vortex agglomeration, (3) jet column self-excited oscillation, (4) shear layer self-excited oscillation,(5) "ordered tearing", (6) turbulence in the case of U1 ＜ 4 m/s (the "ordered tearing" does not exist when U1 ＞ 4m/s), correspondingly, the spatial evolution of the temporal asymptotic behavior of a dynamical system can be described as follows: (1) Hopf bifurcation, (2) subharmonic bifurcation, (3)reversed superharmonic bifurcation, (4) superharmonic bifurcation, (5) chaos ("weak turbulence") in the case of U1 ＜ 4 m/s (superharmonic bifurcation does not exist when U1 ＞ 4 m/s). The proposed new terms, superharmonic and reversed superharmonic bifurcations, are characterized of the frequency doubling rather than the period doubling. A kind of unfamiliar
Axisymmetric multiphase lattice Boltzmann method for generic equations of state
Reijers, Sten Arjen; Gelderblom, Hanneke; Toschi, F.
2016-01-01
We present an axisymmetric lattice Boltzmann model based on the Kupershtokh et al. multiphase model that is capable of solving liquid–gas density ratios up to 103. Appropriate source terms are added to the lattice Boltzmann evolution equation to fully recover the axisymmetric multiphase conservation
Axisymmetric nonconforming element method and its convergence analysis
Institute of Scientific and Technical Information of China (English)
陈万吉; 高岩
1997-01-01
By virtue of the weighted Sobolev space theory, three convergence tests of the axisymmetric non-conforming element method are established. They consist of the generalized patch test, the F-E-M test and a test which could be used conveniently, called the strong patch test (SPT). In the light of SPT, a class of axisymmetric nonconforming elements is established.
Axisymmetric multiphase lattice Boltzmann method for generic equations of state
Reijers, S.A.; Gelderblom, H.; Toschi, F.
2016-01-01
We present an axisymmetric lattice Boltzmann model based on the Kupershtokh et al. multiphase model that is capable of solving liquid–gas density ratios up to 103. Appropriate source terms are added to the lattice Boltzmann evolution equation to fully recover the axisymmetric multiphase conservation
Arbitrary axisymmetric steady streaming: Flow, force and propulsion
Spelman, Tamsin A
2015-01-01
A well-developed method to induce mixing on microscopic scales is to exploit flows generated by steady streaming. Steady streaming is a classical fluid dynamics phenomenon whereby a time-periodic forcing in the bulk or along a boundary is enhanced by inertia to induce a non-zero net flow. Building on classical work for simple geometrical forcing and motivated by the complex shape oscillations of elastic capsules and bubbles, we develop the mathematical framework to quantify the steady streaming of a spherical body with arbitrary axisymmetric time-periodic boundary conditions. We compute the flow asymptotically for small-amplitude oscillations of the boundary in the limit where the viscous penetration length scale is much smaller than the body. In that case, the flow has a boundary layer structure and the fluid motion is solved by asymptotic matching. Our results, presented in the case of no-slip boundary conditions and extended to include the motion of vibrating free surfaces, recovers classical work as parti...
Akinetic rigid syndrome: An overview
Directory of Open Access Journals (Sweden)
Gupta Praveen
2007-01-01
Full Text Available Akinetic-rigid syndromes can be caused by diverse etiologies. It is vital to separate idiopathic Parkinson′s disease from other neurodegenerative diseases and causes of secondary parkinsonism as it has significant therapeutic implications. However even specialists may misdiagnose nonidiopathic parkinsonism as Parkinson′s disease in a quarter of cases. Often the history may be nonspecific and all investigations may be normal. The diagnosis may thus rest entirely on clinical features. The etiological diagnosis of Akinetic rigid syndrome has critical therapeutic and prognostic implications. Therefore we will review the various etiologies of akinetic rigid syndrome and highlight critical clinical features to aid in differential diagnosis.
Institute of Scientific and Technical Information of China (English)
王亚楠; 吕振华
2011-01-01
以商用车动力装置-悬置系统为研究对象，分别建立了动力总成-空调压缩机-悬置系统模型和动力总成-传动轴-悬置系统模型，计算了以上两种多刚体-弹性系统的振动模态，进行了动力总成的刚体振动模态频率关于耦合子系统参数的变化历程分析。计算和实验结果表明：空调压缩机通过其传动带与动力总成的耦合对动力总成的刚体振动模态有显著影响，使得动力总成-悬置系统的刚体振动模态频率提高了，不利于隔振设计目标的实现，但传动轴的影响较小。据此提出了关于动力总成-空调压缩机-悬置系统的弹性耦合刚度匹配改进建议。%The commercial vehicle powertrain dynamics models with multi--rigid--bodies and mounting systems were set up, and the rigid bodies include power plant, AC compressor and propeller shaft. The vi- brational modal characteristics of the multi--rigid--body powertrain with mounting systems were numerically analyzed, and parametrical studies were further carried out. The simulation and experimental modal analysis results show that the rigid--body vibration modes of power plant may be changed noticeably by the AC com- pressor coupled through its flexible driving belt, and therefore several modal frequencies are increased, which negatively affects the power plant vibration isolation. Fortunately, the effect of the propeller shaft inertia is negligible. On the basis of the numerical analysis, a suggestion was presented to improve the elastic coupling stiffness between power plant and AC compressor, etc.
Design of an Axisymmetric Afterbody Test Case for CFD Validation
Disotell, Kevin J.; Rumsey, Christopher L.
2017-01-01
As identified in the CFD Vision 2030 Study commissioned by NASA, validation of advanced RANS models and scale-resolving methods for computing turbulent flow fields must be supported by continuous improvements in fundamental, high-fidelity experiments designed specifically for CFD implementation. In accordance with this effort, the underpinnings of a new test platform referred to herein as the NASA Axisymmetric Afterbody are presented. The devised body-of-revolution is a modular platform consisting of a forebody section and afterbody section, allowing for a range of flow behaviors to be studied on interchangeable afterbody geometries. A body-of-revolution offers advantages in shape definition and fabrication, in avoiding direct contact with wind tunnel sidewalls, and in tail-sting integration to facilitate access to higher Reynolds number tunnels. The current work is focused on validation of smooth-body turbulent flow separation, for which a six-parameter body has been developed. A priori RANS computations are reported for a risk-reduction test configuration in order to demonstrate critical variation among turbulence model results for a given afterbody, ranging from barely-attached to mild separated flow. RANS studies of the effects of forebody nose (with/without) and wind tunnel boundary (slip/no-slip) on the selected afterbody are presented. Representative modeling issues that can be explored with this configuration are the effect of higher Reynolds number on separation behavior, flow physics of the progression from attached to increasingly-separated afterbody flows, and the effect of embedded longitudinal vortices on turbulence structure.
The axisymmetric torsional contact problem of a functionally graded piezoelectric coated half-space
Su, Jie; Ke, Liao-Liang; Wang, Yue-Sheng; Xiang, Yang
2017-01-01
In this article, we study the axisymmetric torsional contact problem of a half-space coated with functionally graded piezoelectric material (FGPM) and subjected to a rigid circular punch. It is found that, along the thickness direction, the electromechanical properties of FGPMs change exponentially. We apply the Hankel integral transform technique and reduce the problem to a singular integral equation, and then numerically determine the unknown contact stress and electric displacement at the contact surface. The results show that the surface contact stress, surface azimuthal displacement, surface electric displacement, and inner electromechanical field are obviously dependent on the gradient index of the FGPM coating. It is found that we can adjust the gradient index of the FGPM coating to modify the distributions of the electric displacement and contact stress.
Unsteady heat transfer in non-axisymmetric Homann stagnation-point flows
Mahapatra, T. R.; Sidui, S.
2017-04-01
An analysis is carried out to study the unsteady non-axisymmetric Homann's stagnation-point flow and heat transfer of an incompressible viscous fluid over a rigid plate in the presence of time-dependent free stream. The temperature of the plate is assumed to be higher than the ambient fluid temperature. Using similarity variables, the governing partial differential equations are transformed into nonlinear ordinary differential equations. These equations are then solved numerically using fourth-order Runge-Kutta method with shooting technique. The effects of the shear-to-strain rate ratio parameter γ (γ =b/a where a and b are the strain rate and shear rate of the stagnation-point flow, respectively) and the unsteadiness parameter λ on wall shear stress parameters, dimensionless velocities, rate of heat transfer at the wall and dimensionless temperature are analysed. It is found that the large-γ asymptotes do not depend on the parameter λ.
A solvable model of axisymmetric and non-axisymmetric droplet bouncing.
Andrew, Matthew; Yeomans, Julia M; Pushkin, Dmitri O
2017-02-07
We introduce a solvable Lagrangian model for droplet bouncing. The model predicts that, for an axisymmetric drop, the contact time decreases to a constant value with increasing Weber number, in qualitative agreement with experiments, because the system is well approximated as a simple harmonic oscillator. We introduce asymmetries in the velocity, initial droplet shape, and contact line drag acting on the droplet and show that asymmetry can often lead to a reduced contact time and lift-off in an elongated shape. The model allows us to explain the mechanisms behind non-axisymmetric bouncing in terms of surface tension forces. Once the drop has an elliptical footprint the surface tension force acting on the longer sides is greater. Therefore the shorter axis retracts faster and, due to the incompressibility constraints, pumps fluid along the more extended droplet axis. This leads to a positive feedback, allowing the drop to jump in an elongated configuration, and more quickly.
Skeletal Rigidity of Phylogenetic Trees
Cheng, Howard; Li, Brian; Risteski, Andrej
2012-01-01
Motivated by geometric origami and the straight skeleton construction, we outline a map between spaces of phylogenetic trees and spaces of planar polygons. The limitations of this map is studied through explicit examples, culminating in proving a structural rigidity result.
Direct numerical simulation of axisymmetric turbulence
Qu, Bo; Bos, Wouter J. T.; Naso, Aurore
2017-09-01
The dynamics of decaying, strictly axisymmetric, incompressible turbulence is investigated using direct numerical simulations. It is found that the angular momentum is a robust invariant of the system. It is further shown that long-lived coherent structures are generated by the flow. These structures can be associated with stationary solutions of the Euler equations. The structures obey relations in agreement with predictions from selective decay principles, compatible with the decay laws of the system. Two different types of decay scenarios are highlighted. The first case results in a quasi-two-dimensional flow with a dynamical behavior in the poloidal plane similar to freely decaying two-dimensional turbulence. In a second regime, the long-time dynamics is dominated by a single three-dimensional mode.
Nonlinear axisymmetric liquid currents in spherical annuli
Astafyeva, N. M.; Vvedenskaya, N. D.; Yavorskaya, I. M.
1978-01-01
A numerical analysis of non-linear axisymmetric viscous flows in spherical annuli of different gap sizes is presented. Only inner sphere was supposed to rotate at a constant angular velocity. The streamlines, lines of constant angular velocity, kinetic energy spectra, and spectra of velocity components are obtained. A total kinetic energy and torque needed to rotate the inner sphere are calculated as functions of Re for different gap sizes. In small-gap annulus nonuniqueness of steady solutions of Navier-Stokes equations is established and regions of different flow regime existences are found. Numerical solutions in a wide-gap annulus and experimental results are used in conclusions about flow stability in the considered range of Re. The comparison of experimental and numerical results shows close qualitative and quantitative agreement.
Lagrangian mixing in an axisymmetric hurricane model
Directory of Open Access Journals (Sweden)
B. Rutherford
2009-09-01
Full Text Available This paper discusses the extension of established Lagrangian mixing measures to make them applicable to data extracted from a 2-D axisymmetric hurricane simulation. Because of the non-steady and unbounded characteristics of the simulation, the previous measures are extended to a moving frame approach to create time-dependent mixing rates that are dependent upon the initial time of particle integration, and are computed for nonlocal regions. The global measures of mixing derived from finite-time Lyapunov exponents, relative dispersion, and a measured mixing rate are applied to distinct regions representing different characteristic feautures within the model. It is shown that these time-dependent mixing rates exhibit correlations with maximal tangential winds during a quasi-steady state, establishing a connection between mixing and hurricane intensity.
Wage rigidity and job creation
Haefke, Christian; Sonntag, Marcus; Rens, Thijs van
2013-01-01
Recent research in macroeconomics emphasizes the role of wage rigidity in accounting for the volatility of unemployment fluctuations. We use worker-level data from the CPS to measure the sensitivity of wages of newly hired workers to changes in aggregate labor market conditions. The wage of new hires, unlike the aggregate wage, is volatile and responds almost one-to-one to changes in labor productivity. We conclude that there is little evidence for wage rigidity in the data.
Axisymmetric Plume Simulations with NASA's DSMC Analysis Code
Stewart, B. D.; Lumpkin, F. E., III
2012-01-01
A comparison of axisymmetric Direct Simulation Monte Carlo (DSMC) Analysis Code (DAC) results to analytic and Computational Fluid Dynamics (CFD) solutions in the near continuum regime and to 3D DAC solutions in the rarefied regime for expansion plumes into a vacuum is performed to investigate the validity of the newest DAC axisymmetric implementation. This new implementation, based on the standard DSMC axisymmetric approach where the representative molecules are allowed to move in all three dimensions but are rotated back to the plane of symmetry by the end of the move step, has been fully integrated into the 3D-based DAC code and therefore retains all of DAC s features, such as being able to compute flow over complex geometries and to model chemistry. Axisymmetric DAC results for a spherically symmetric isentropic expansion are in very good agreement with a source flow analytic solution in the continuum regime and show departure from equilibrium downstream of the estimated breakdown location. Axisymmetric density contours also compare favorably against CFD results for the R1E thruster while temperature contours depart from equilibrium very rapidly away from the estimated breakdown surface. Finally, axisymmetric and 3D DAC results are in very good agreement over the entire plume region and, as expected, this new axisymmetric implementation shows a significant reduction in computer resources required to achieve accurate simulations for this problem over the 3D simulations.
The Mechanics of Axisymmetric Indentation Revisited
2013-07-01
were among the first to consider such a problem, but Sneddon (4, 8) solved the mixed boundary value problem for the rigid flat-ended punch in...punch. This result has been obtained by both England (21; page 70, equation (3.67)) using complex variable methods, and Sneddon (1; page 433, equation...report for readers interested in such analysis. Furthermore, the original works of Sneddon (1, 4, 8) lacked analytical expressions for the vertical
Growth of axisymmetric instabilities in ASDEX upgrade
Energy Technology Data Exchange (ETDEWEB)
Sehmer, Till; Lackner, Karl; Strumberger, Erika; Fable, Emiliano; Kardaun, Otto [Max-Planck-Institut fuer Plasma-Physik, EURATOM Association Boltzmannstrasse 2, 85748 Garching (Germany); McCarthy, Patrick [University College Cork (Ireland)
2014-07-01
Modern poloidal divertor tokamaks, such as ASDEX upgrade (AUG), produce elongated plasmas, which are unstable against vertical displacement. The growth rate of this 2D instability in the presence of stabilizing passive conductors (PSL) with finite resistivity was calculated for 5416 AUG typical equilibria. For this, a general ideal MHD code package (NEMEC, CAS3DN, STARWALL) was used, which is able to take into account also the 3D structure of the PSL. The comparison of the resulting growth rates with the previously used rigid displacement model (movement only in z-direction, no skin effect for PSL considered, no induced surface currents) shows that the latter simplified model gives a consistently lower limit for typical AUG parameters (elongation, triangularity, current profile and axis position in radial direction). A statistical analysis of the results of the rigid displacement model shows the expected dependencies except for the triangularity, which has a stabilizing effect in this model. Based on results of our present, more general model, we conclude that a rigid displacement model gives an over-optimistic result regarding the effect of triangularity, in line with the experimental observation on AUG of an increasing discrepancy between previously predicted and observed growth rates for strongly triangular plasmas.
Emergency Entry with One Control Torque: Non-Axisymmetric Diagonal Inertia Matrix
Llama, Eduardo Garcia
2011-01-01
In another work, a method was presented, primarily conceived as an emergency backup system, that addressed the problem of a space capsule that needed to execute a safe atmospheric entry from an arbitrary initial attitude and angular rate in the absence of nominal control capability. The proposed concept permits the arrest of a tumbling motion, orientation to the heat shield forward position and the attainment of a ballistic roll rate of a rigid spacecraft with the use of control in one axis only. To show the feasibility of such concept, the technique of single input single output (SISO) feedback linearization using the Lie derivative method was employed and the problem was solved for different number of jets and for different configurations of the inertia matrix: the axisymmetric inertia matrix (I(sub xx) > I(sub yy) = I(sub zz)), a partially complete inertia matrix with I(sub xx) > I(sub yy) > I(sub zz), I(sub xz) not = 0 and a realistic complete inertia matrix with I(sub xx) > I(sub yy) > I)sub zz), I(sub ij) not= 0. The closed loop stability of the proposed non-linear control on the total angle of attack, Theta, was analyzed through the zero dynamics of the internal dynamics for the case where the inertia matrix is axisymmetric (I(sub xx) > I(sub yy) = I(sub zz)). This note focuses on the problem of the diagonal non-axisymmetric inertia matrix (I(sub xx) > I(sub yy) > I(sub zz)), which is half way between the axisymmetric and the partially complete inertia matrices. In this note, the control law for this type of inertia matrix will be determined and its closed-loop stability will be analyzed using the same methods that were used in the other work. In particular, it will be proven that the control system is stable in closed-loop when the actuators only provide a roll torque.
Asymmetric and axisymmetric dynamics of tropical cyclones
Directory of Open Access Journals (Sweden)
J. Persing
2013-05-01
Full Text Available We present the results of idealized numerical experiments to examine the difference between tropical cyclone evolution in three-dimensional (3-D and axisymmetric (AX model configurations. We focus on the prototype problem for intensification, which considers the evolution of an initially unsaturated AX vortex in gradient-wind balance on an f-plane. Consistent with findings of previous work, the mature intensity in the 3-D model is reduced relative to that in the AX model. In contrast with previous interpretations invoking barotropic instability and related horizontal mixing processes as a mechanism detrimental to the spin-up process, the results indicate that 3-D eddy processes associated with vortical plume structures can assist the intensification process by contributing to a radial contraction of the maximum tangential velocity and to a vertical extension of tangential winds through the depth of the troposphere. These plumes contribute significantly also to the azimuthally-averaged heating rate and the corresponding azimuthal-mean overturning circulation. The comparisons show that the resolved 3-D eddy momentum fluxes above the boundary layer exhibit counter-gradient characteristics and are generally not represented properly by the subgrid-scale parameterizations in the AX configuration. The resolved eddy fluxes act to support the contraction and intensification of the maximum tangential winds. The comparisons indicate fundamental differences between convective organization in the 3-D and AX configurations for meteorologically relevant forecast time scales. While the radial and vertical gradients of the system-scale angular rotation provide a hostile environment for deep convection in the 3-D model, with a corresponding tendency to strain the convective elements in the tangential direction, deep convection in the AX model does not suffer this tendency. Also, since during the 3-D intensification process the convection has not yet organized
Modeling and simulation of axisymmetric stagnation flames
Sone, Kazuo
Laminar flame modeling is an important element in turbulent combustion research. The accuracy of a turbulent combustion model is highly dependent upon our understanding of laminar flames and their behavior in many situations. How much we understand combustion can only be measured by how well the model describes and predicts combustion phenomena. One of the most commonly used methane combustion models is GRI-Mech 3.0. However, how well the model describes the reacting flow phenomena is still uncertain even after many attempts to validate the model or quantify uncertainties. In the present study, the behavior of laminar flames under different aerodynamic and thermodynamic conditions is studied numerically in a stagnation-flow configuration. In order to make such a numerical study possible, the spectral element method is reformulated to accommodate the large density variations in methane reacting flows. In addition, a new axisymmetric basis function set for the spectral element method that satisfies the correct behavior near the axis is developed, and efficient integration techniques are developed to accurately model axisymmetric reacting flow within a reasonable amount of computational time. The numerical method is implemented using an object-oriented programming technique, and the resulting computer program is verified with several different verification methods. The present study then shows variances with the commonly used GRI-Mech 3.0 chemical kinetics model through a direct simulation of laboratory flames that allows direct comparison to experimental data. It is shown that the methane combustion model based on GRI-Mech 3.0 works well for methane-air mixtures near stoichiometry. However, GRI-Mech 3.0 leads to an overprediction of laminar flame speed for lean mixtures and an underprediction for rich mixtures. This result is slightly different from conclusion drawn in previous work, in which experimental data are compared with a one-dimensional numerical solutions
Axisymmetric Magnetic Mirror Fusion-Fission Hybrid
Energy Technology Data Exchange (ETDEWEB)
Moir, R. W. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Martovetsky, N. N. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Molvik, A. W. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Ryutov, D. D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Simonen, T. C. [Univ. of California, Berkeley, CA (United States)
2011-05-13
The achieved performance of the gas dynamic trap version of magnetic mirrors and today’s technology we believe are sufficient with modest further efforts for a neutron source for material testing (Q=P_{fusion}/P_{input}~0.1). The performance needed for commercial power production requires considerable further advances to achieve the necessary high Q>>10. An early application of the mirror, requiring intermediate performance and intermediate values of Q~1 are the hybrid applications. The Axisymmetric Mirror has a number of attractive features as a driver for a fusion-fission hybrid system: geometrical simplicity, inherently steady-state operation, and the presence of the natural divertors in the form of end tanks. This level of physics performance has the virtue of low risk and only modest R&D needed and its simplicity promises economy advantages. Operation at Q~1 allows for relatively low electron temperatures, in the range of 4 keV, for the DT injection energy ~ 80 keV. A simple mirror with the plasma diameter of 1 m and mirror-to-mirror length of 35 m is discussed. Simple circular superconducting coils are based on today’s technology. The positive ion neutral beams are similar to existing units but designed for steady state. A brief qualitative discussion of three groups of physics issues is presented: axial heat loss, MHD stability in the axisymmetric geometry, microstability of sloshing ions. Burning fission reactor wastes by fissioning actinides (transuranics: Pu, Np, Am, Cm, .. or just minor actinides: Np, Am, Cm, …) in the hybrid will multiply fusion’s energy by a factor of ~10 or more and diminish the Q needed to less than 1 to overcome the cost of recirculating power for good economics. The economic value of destroying actinides by fissioning is rather low based on either the cost of long-term storage or even deep geologic disposal so most of the revenues of hybrids will come from electrical power. Hybrids that obtain revenues from
Numerical Strategies for Stroke Optimization of Axisymmetric Microswimmers
Alouges, François; Heltai, Luca
2009-01-01
We propose a computational method to solve optimal swimming problems, based on the boundary integral formulation of the hydrodynamic interaction between swimmer and surrounding fluid and direct constrained minimization of the energy consumed by the swimmer. We apply our method to axisymmetric model examples. We consider a classical model swimmer (the three-sphere swimmer of Golestanian et al.) as well as a novel axisymmetric swimmer inspired by the observation of biological micro-organisms.
Rigidly foldable origami gadgets and tessellations.
Evans, Thomas A; Lang, Robert J; Magleby, Spencer P; Howell, Larry L
2015-09-01
Rigidly foldable origami allows for motion where all deflection occurs at the crease lines and facilitates the application of origami in materials other than paper. In this paper, we use a recently discovered method for determining rigid foldability to identify existing flat-foldable rigidly foldable tessellations, which are also categorized. We introduce rigidly foldable origami gadgets which may be used to modify existing tessellations or to create new tessellations. Several modified and new rigidly foldable tessellations are presented.
Rigidly foldable origami gadgets and tessellations
Evans, Thomas A.; Lang, Robert J.; Magleby, Spencer P.; Howell, Larry L.
2015-01-01
Rigidly foldable origami allows for motion where all deflection occurs at the crease lines and facilitates the application of origami in materials other than paper. In this paper, we use a recently discovered method for determining rigid foldability to identify existing flat-foldable rigidly foldable tessellations, which are also categorized. We introduce rigidly foldable origami gadgets which may be used to modify existing tessellations or to create new tessellations. Several modified and new rigidly foldable tessellations are presented. PMID:26473037
Non-Axisymmetric Inflatable Pressure Structure (NAIPS) Full-Scale Pressure Test
Jones, Thomas C.; Doggett, William R.; Warren, Jerry E.; Watson, Judith J.; Shariff, Khadijah; Makino, Alberto; Yount, Bryan C.
2017-01-01
Inflatable space structures have the potential to significantly reduce the required launch volume for large pressure vessels required for exploration applications including habitats, airlocks and tankage. In addition, mass savings can be achieved via the use of high specific strength softgoods materials, and the reduced design penalty from launching the structure in a densely packaged state. Large inclusions however, such as hatches, induce a high mass penalty at the interfaces with the softgoods and in the added rigid structure while reducing the packaging efficiency. A novel, Non-Axisymmetric Inflatable Pressure Structure (NAIPS) was designed and recently tested at NASA Langley Research Center to demonstrate an elongated inflatable architecture that could provide areas of low stress along a principal axis in the surface. These low stress zones will allow the integration of a flexible linear seal that substantially reduces the added mass and volume of a heritage rigid hatch structure. This paper describes the test of the first full-scale engineering demonstration unit (EDU) of the NAIPS geometry and a comparison of the results to finite element analysis.
Axisymmetric Vortex Simulations with Various Turbulence Models
Directory of Open Access Journals (Sweden)
Brian Howard Fiedler
2010-10-01
Full Text Available The CFD code FLUENT^{TM} has been applied to a vortex within an updraft above a frictional lower boundary. The sensitivity of vortex intensity and structure to the choice of turbulent model is explored. A high Reynolds number of 10^{8} is employed to make the investigation relevant to the atmospheric vortex known as a tornado. The simulations are axisymmetric and are integrated forward in time to equilibrium. In a variety of turbulence models tested, the Reynolds Stress Model allows for the greatest intensification of the vortex, with the azimuthal wind speed near the surface being 2.4 times the speed of the updraft, consistent with the destructive nature of tornadoes. The Standard k-e Model, which is simpler than the Reynolds Stress Model but still more detailed than what is commonly available in numerical weather prediction models, produces an azimuthal wind speed near the surface of at most 0.6 times the updraft speed.
Vortexons in axisymmetric Poiseuille pipe flows
Fedele, Francesco
2012-01-01
We present a study on the nonlinear dynamics of small long-wave disturbances to the laminar state in non-rotating axisymmetric Poiseuille pipe flows. At high Reynolds numbers, the associated Navier-Stokes equations can be reduced to a set of coupled Korteweg-de Vries-type (KdV) equations that support inviscid and smooth travelling waves numerically computed using the Petviashvili method. In physical space they correspond to localized toroidal vortices concentrated near the pipe boundaries (wall vortexons) or that wrap around the pipe axis (centre vortexons), in agreement with the analytical soliton solutions derived by Fedele (2012). The KdV dynamics of a perturbation is also investigated by means of an high accurate Fourier-based numerical scheme. We observe that an initial vortical patch splits into a centre vortexon radiating patches of vorticity near the wall. These can undergo further splitting leading to a proliferation of centre vortexons that eventually decay due to viscous effects. The splitting proc...
Reese, D; Rieutord, M
2004-01-01
We carry out numerical and mathematical investigations of shear Alfven waves inside of a spherical shell filled with an incompressible conducting fluid, and bathed in a strong dipolar magnetic field. We focus on axisymmetric toroidal and non-axisymmetric modes, in continuation of a previous work by Rincon & Rieutord (2003). Analytical expressions are obtained for toroidal eigenmodes and their corresponding frequencies at low diffusivities. These oscillations behave like magnetic shear layers, in which the magnetic poles play a key role, and hence become singular when diffusivities vanish. It is also demonstrated that non-axisymmetric modes are split into two categories, namely poloidal or toroidal types, following similar asymptotic behaviours as their axisymmetric counterparts when the diffusivities become arbitrarily small.
Institute of Scientific and Technical Information of China (English)
王刚; 刘延杰; 吴明月; 韩海军
2015-01-01
Targeting a Delta parallel robot which is widely used for high speed pick and place operation,a novel approximation for simpli-fied rigid body dynamic model based on Lagrangian multiplier method is established.Both of the in-verse kinematic and rigid dynamic model are devel-oped,and the dynamic model is simplified consid-ering the actual situation of the robot.Comparing the calculation results of the dynamic model before and after the simplification with the simulation re-sults show that the simplified rigid model can not only reduce the amount of calculation but also im-prove the accuracy of it.%针对广泛应用于高速抓放操作的 Delta并联机器人，提出了一种基于拉格朗日乘子法的刚体动力学建模方法，并利用约束方程的全微分求解出了动力学模型的显示表达式。建立了机器人的逆运动学以及刚体动力学模型，考虑机器人从动臂臂杆为轻质碳纤维杆，两端为较重的金属附件的特点，建立了简化刚体动力学模型。并针对机器人常用的高速抓放轨迹进行仿真，将简化前后的2种动力学模型与 ADAMS 仿真结果进行对比。
DEFF Research Database (Denmark)
Rijkhoff, Jan
2008-01-01
, Non-Verb, Modifier), there are also flexible word classes within the rigid lexical category Noun (Set Noun, Sort Noun, General Noun). Members of flexible word classes are characterized by their vague semantics, which in the case of nouns means that values for the semantic features Shape...
DEFF Research Database (Denmark)
Rijkhoff, Jan
2010-01-01
This article argues that in addition to the major flexible lexical categories in Hengeveld’s classification of parts of speech systems (Contentive, Non-Verb, Modifier), there are also flexible word classes within the rigid lexical category Noun (Set Noun, Sort Noun, General Noun). Members...
Rigidity-tuning conductive elastomer
Shan, Wanliang; Diller, Stuart; Tutcuoglu, Abbas; Majidi, Carmel
2015-06-01
We introduce a conductive propylene-based elastomer (cPBE) that rapidly and reversibly changes its mechanical rigidity when powered with electrical current. The elastomer is rigid in its natural state, with an elastic (Young’s) modulus of 175.5 MPa, and softens when electrically activated. By embedding the cPBE in an electrically insulating sheet of polydimethylsiloxane (PDMS), we create a cPBE-PDMS composite that can reversibly change its tensile modulus between 37 and 1.5 MPa. The rigidity change takes ˜6 s and is initiated when a 100 V voltage drop is applied across the two ends of the cPBE film. This magnitude of change in elastic rigidity is similar to that observed in natural skeletal muscle and catch connective tissue. We characterize the tunable load-bearing capability of the cPBE-PDMS composite with a motorized tensile test and deadweight experiment. Lastly, we demonstrate the ability to control the routing of internal forces by embedding several cPBE-PDMS ‘active tendons’ into a soft robotic pneumatic bending actuator. Selectively activating the artificial tendons controls the neutral axis and direction of bending during inflation.
Rigid coupling is also flexible
Appleberry, W. T.
1978-01-01
Spring-loaded coupling is rigid under light loads and swivels under higher loads. Break-out point can be set at any desired value by selecting appropriate preload springs. Coupling requires no cushions or elastomeric joints that limit temperature range.
MODAL ACOUSTIC IMPEDANCE FORCE ON A SPHERICAL SOURCE NEAR A RIGID INTERFACE
Institute of Scientific and Technical Information of China (English)
Seyyed M. HASHEMINEJAD
2003-01-01
The modal acoustic radiation load on a spherical surface undergoing angularly periodic axisymmetric harmonic vibrations while immersed in an acoustic halfspace with a rigid (infinite impedance) planar boundary is analyzed in an exact fashion using the classical technique of separation of variables. The formulation utilizes the appropriate wave field expansions, the classical method of images and the appropriate translational addition theorem to simulate the relevant boundary conditions for the given configuration. The associated acoustic field quantities such as the modal impedance matrix and the modal acoustic radiation force acting on the spherical surface are determined. The analytical results are illustrated with a numerical example in which the spherical surface, excited in vibrational modes of various orders, is immersed near an impervious rigid wall. The presented solution could eventually be used to validate those obtained by numerical approximation techniques.
Fast electron bremsstrahlung in axisymmetric magnetic configuration
Peysson, Y.; Decker, J.
2008-09-01
The nonthermal bremsstrahlung is calculated in a plasma with arbitrary axisymmetric magnetic configuration, taking into account the relativistic angular anisotropy of the radiation cross section at high photon energies, the helical winding of the field lines on the magnetic flux surfaces, and the poloidal variation of the electron distribution function including particle trapping effects. The fast electron dynamics during current drive in tokamaks and reverse field pinches can be investigated in detail by coupling this calculation to a bounce-averaged relativistic Fokker-Planck solver, which calculates the electron distribution function. The asymmetry between high- and low-field side hard x-ray emission intensity that has been measured on the Tore-Supra tokamak [Equipe TORE SUPRA, in Proceedings of the 15th Conference on Plasma Physics and Controlled Nuclear Fusion Research, Seville (International Atomic Energy Agency, Vienna, 1995) Vol. 1, IAEA-CN-60/A1-5 (Institute of Physics, Bristol, U.K., 1995), p. 105] is explained for the first time by the role of trapped electrons. A much stronger poloidal asymmetry is predicted for the line-integrated fast electron bremsstrahlung in the poloidal plane of the Madison Symmetric Torus [R. N. Dexter et al., Fusion Tech. 19, 131 (1991)], since the helical winding of the magnetic field lines is much larger for a reverse field pinch configuration. In this case, the hard x-ray emission is no longer a flux surface quantity, which prevents local reconstructions using a standard Abel inversion, whatever the geometrical arrangement of the lines of sight.
Interactive Perception of Rigid and Non-Rigid Objects
Directory of Open Access Journals (Sweden)
Bryan Willimon
2012-12-01
Full Text Available This paper explores the concept of interactive perception, in which sensing guides manipulation, in the context of extracting and classifying unknown objects within a cluttered environment. In the proposed approach, a pile of objects lies on a flat background, and the goal of the robot is to isolate, interact with, and classify each object so that its properties can be obtained. The algorithm considers each object to be classified using color, shape, and flexibility. The approach works with a variety of objects relevant to service robot applications, including both rigid objects such as bottles, cans, and pliers as well as non‐rigid objects such as soft toy animals, socks, and shoes. Experiments on a number of different piles of objects demonstrate the ability of efficiently isolating and classifying each item through interaction.
A rigid surface boundary element for soil-structure interaction analysis in the direct time domain
Rizos, D. C.
Many soil-structure interaction problems involve studies of single or multiple rigid bodies of arbitrary shape and soil media. The commonly used boundary element methods implement the equations of the rigid body in a form that depends on the particulars of the geometry and requires partitioning and condensation of the associated algebraic system of equations. The present work employs the direct time domain B-Spline BEM for 3D elastodynamic analysis and presents an efficient implementation of rigid bodies of arbitrary shape in contact with, or embedded in, elastic media. The formulation of a rigid surface boundary element introduced herein is suitable for direct superposition in the BEM system of algebraic equations. Consequently, solutions are computed in a single analysis step, eliminating, thus, the need for partitioning of the system of equations. Computational efficiency is also achieved due to the extremely sparse form of the associated coefficient matrices. The proposed element can be used for the modeling of single or multiple rigid bodies of arbitrary shape within the framework of the BEM method. The efficiency and general nature of the proposed element is demonstrated through applications related to the dynamic analysis of rigid surface and embedded foundations and their interaction with embedded rigid bodies of arbitrary shape.
Discrete Time Crystals: Rigidity, Criticality, and Realizations
Yao, N. Y.; Potter, A. C.; Potirniche, I.-D.; Vishwanath, A.
2017-01-01
Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry. The period of the resulting discrete time crystal is quantized to an integer multiple of the drive period, arising from a combination of collective synchronization and many body localization. Here, we consider a simple model for a one-dimensional discrete time crystal which explicitly reveals the rigidity of the emergent oscillations as the drive is varied. We numerically map out its phase diagram and compute the properties of the dynamical phase transition where the time crystal melts into a trivial Floquet insulator. Moreover, we demonstrate that the model can be realized with current experimental technologies and propose a blueprint based upon a one dimensional chain of trapped ions. Using experimental parameters (featuring long-range interactions), we identify the phase boundaries of the ion-time-crystal and propose a measurable signature of the symmetry breaking phase transition.
Discrete Time Crystals: Rigidity, Criticality, and Realizations.
Yao, N Y; Potter, A C; Potirniche, I-D; Vishwanath, A
2017-01-20
Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry. The period of the resulting discrete time crystal is quantized to an integer multiple of the drive period, arising from a combination of collective synchronization and many body localization. Here, we consider a simple model for a one-dimensional discrete time crystal which explicitly reveals the rigidity of the emergent oscillations as the drive is varied. We numerically map out its phase diagram and compute the properties of the dynamical phase transition where the time crystal melts into a trivial Floquet insulator. Moreover, we demonstrate that the model can be realized with current experimental technologies and propose a blueprint based upon a one dimensional chain of trapped ions. Using experimental parameters (featuring long-range interactions), we identify the phase boundaries of the ion-time-crystal and propose a measurable signature of the symmetry breaking phase transition.
Rigid subsets of symplectic manifolds
Entov, Michael
2007-01-01
We show that there is an hierarchy of intersection rigidity properties of sets in a closed symplectic manifold: some sets cannot be displaced by symplectomorphisms from more sets than the others. We also find new examples of rigidity of intersections involving, in particular, specific fibers of moment maps of Hamiltonian torus actions, monotone Lagrangian submanifolds (following the previous work of P.Albers) as well as certain, possibly singular, sets defined in terms of Poisson-commutative subalgebras of smooth functions. In addition, we get some geometric obstructions to semi-simplicity of the quantum homology of symplectic manifolds. The proofs are based on the Floer-theoretical machinery of partial symplectic quasi-states.
Rigidity spectrum of Forbush decrease
Sakakibara, S.; Munakata, K.; Nagashima, K.
1985-01-01
Using data from neutron monitors and muon telescopes at surface and underground stations, the average rigidity spectrum of Forbush decreases (Fds) during the period of 1978-1982 were obtained. Thirty eight Ed-events are classified into two groups Hard Fd and Soft Fd according to size of Fd at Sakashita station. It is found that a spectral form of fractional-power type (P to the-gamma sub 1 (P+P sub c) to the -gamma sub2) is more suitable for the present purpose than that of power-exponential type or of power type with an upper limiting rigidity. The best fitted spectrum of fractional-power type is expressed by gamma sub1 = 0.37, gamma sub2 = 0.89 and P subc = 10 GV for Hard Fd and gamma sub1 = 0.77, gamma sub2 = 1.02 and P sub c - 14GV for Soft Fd.
Near surface stress analysis strategies for axisymmetric fretting
Indian Academy of Sciences (India)
M Ramesh; Satish V Kailas; K R Y Simha
2008-06-01
Fretting is essentially a surface phenomenon, but bulk stresses and material properties contribute to subsequent failure. This feature of fretting demands a thorough understanding of near surface stresses under the joint action of normal, shear and thermal loading. Axisymmetric fretting is of great concern in piping and coupling design. In this paper, we develop design tools for Near Surface Analysis (NSA) for understanding axisymmetric fretting. Axisymmetric Fretting Analysis (AFA) becomes formidable owing to localised tractions that call for Fourier transform techniques. We develop two different NSA strategies based on two-dimensional plane strain models: 2D strip model (2DS) and half-plane Flamant model (2DF). We compare the results of 2DS and 2DF with the exact results for AFA obtained using Love’s stress function in conjunction with Fourier transform. There is a good correspondence between stress components obtained from 2D-models.
Stability of a Class of Coupled Rigid-elastic Systems With Symmetry-breaking
Institute of Scientific and Technical Information of China (English)
程耀; 黄克累; 陆启韶
1994-01-01
In this paper, the Poisson structures and Casimir functions, which play an important role in stability analysis of stationary motions, are given for a class of coupled rigid-elastic systems with symmetry-breaking. As a practical example, the specific Casimir function is given for a rigid-elastic coupled body with a fixed point subjected to gravitational force. At last, a set of sufficient conditions for stability of stationary motions of a rigid-elastic body in a circular orbit are given by the energy-Casimir method.
Lablanche, Pierre-Yves; Emsellem, Eric; Bournaud, Frederic; Michel-Dansac, Leo; Alatalo, Katherine; Blitz, Leo; Bois, Maxime; Bureau, Martin; Davies, Roger L; Davis, Timothy A; de Zeeuw, P T; Duc, Pierre-Alain; Khochfar, Sadegh; Krajnovic, Davor; Kuntschner, Harald; Morganti, Raffaella; McDermid, Richard M; Naab, Thorsten; Oosterloo, Tom; Sarzi, Marc; Scott, Nicholas; Serra, Paolo; Weijmans, Anne-Marie; Young, Lisa M
2012-01-01
We investigate the accuracy in the recovery of the stellar dynamics of barred galaxies when using axisymmetric dynamical models. We do this by trying to recover the mass-to-light ratio (M/L) and the anisotropy of realistic galaxy simulations using the Jeans Anisotropic Multi-Gaussian Expansion (JAM) method. However, given that the biases we find are mostly due to an application of an axisymmetric modeling algorithm to a non-axisymmetric system and in particular to inaccuracies in the de-projected mass model, our results are relevant for general axisymmetric modelling methods. We run N-body collisionless simulations to build a library with various luminosity distribution, constructed to mimic real individual galaxies, with realistic anisotropy. The final result of our evolved library of simulations contains both barred and unbarred galaxies. The JAM method assumes an axisymmetric mass distribution, and we adopt a spatially constant M/L and anisotropy beta_z=1-sigma_z^2/sigma_R^2 distributions. The models are f...
Calculating ensemble averaged descriptions of protein rigidity without sampling.
Directory of Open Access Journals (Sweden)
Luis C González
Full Text Available Previous works have demonstrated that protein rigidity is related to thermodynamic stability, especially under conditions that favor formation of native structure. Mechanical network rigidity properties of a single conformation are efficiently calculated using the integer body-bar Pebble Game (PG algorithm. However, thermodynamic properties require averaging over many samples from the ensemble of accessible conformations to accurately account for fluctuations in network topology. We have developed a mean field Virtual Pebble Game (VPG that represents the ensemble of networks by a single effective network. That is, all possible number of distance constraints (or bars that can form between a pair of rigid bodies is replaced by the average number. The resulting effective network is viewed as having weighted edges, where the weight of an edge quantifies its capacity to absorb degrees of freedom. The VPG is interpreted as a flow problem on this effective network, which eliminates the need to sample. Across a nonredundant dataset of 272 protein structures, we apply the VPG to proteins for the first time. Our results show numerically and visually that the rigidity characterizations of the VPG accurately reflect the ensemble averaged [Formula: see text] properties. This result positions the VPG as an efficient alternative to understand the mechanical role that chemical interactions play in maintaining protein stability.
Local Axisymmetric Instability Criterion in the Thin, Rotating, Multicomponent Disk
Rafikov, R R
2000-01-01
Purely gravitational perturbations are considered in a thin rotating disk composed of several gas and stellar components. The dispersion relation for the axisymmetric density waves propagating through the disk is found and the criterion for the local axisymmetric stability of the whole system is formulated. In the appropriate limit of two-component gas we confirm the findings of Jog & Solomon (1984) and extend consideration to the case when one component is collisionless. Gravitational stability of the Galactic disk in the Solar neighborhood based on the multicomponent instability condition is explored using recent measurements of the stellar composition and kinematics in the local Galactic disk obtained by Hipparcos satellite.
Axisymmetric multiphase Lattice Boltzmann method for generic equations of state
Reijers, Sten A; Toschi, Federico
2015-01-01
We present an axisymmetric lattice Boltzmann model based on the Kupershtokh et al. multiphase model that is capable of solving liquid-gas density ratios up to $10^3$. Appropriate source terms are added to the lattice Boltzmann evolution equation to fully recover the axisymmetric multiphase conservation equations. We validate the model by showing that a stationary droplet obeys the Young-Laplace law, comparing the second oscillation mode of a droplet with respect to an analytical solution and showing correct mass conservation of a propagating density wave.
Ion temperature gradient turbulence in helical and axisymmetric RFP plasmas
Predebon, I
2015-01-01
Turbulence induced by the ion temperature gradient (ITG) is investigated in the helical and axisymmetric plasma states of a reversed field pinch device by means of gyrokinetic calculations. The two magnetic configurations are systematically compared, both linearly and nonlinearly, in order to evaluate the impact of the geometry on the instability and its ensuing transport, as well as on the production of zonal flows. Despite its enhanced confinement, the high-current helical state demonstrates a lower ITG stability threshold compared to the axisymmetric state, and ITG turbulence is expected to become an important contributor to the total heat transport.
SIMULATIONS OF FLOWFIELDS AROUND UNDERWATER APPENDED BODIES
Institute of Scientific and Technical Information of China (English)
Huang Zhen-yu; Cheng Hong-rong; Zhou Lian-di; Miao Guo-ping
2003-01-01
The numerical method which is based on flux difference splitting, LU decomposition, and implicit high-resolution third-order Essentially Non-Oscillatory (ENO) scheme was constructed for the efficient computation of steady state solution to three-dimensional incompressible Navier-Stokes equations in general coordinates. The flowfields over underwater axisymmetric bodies, full-appended axisymmetric bodies and axisymetric bodies with a ring-wing duct were simulated. The method is proved to be capable of predicting the circumferential-mean velocity distribution at model scale to the accuracy of around 3% of measured values, and of predicting some details of flow features, for example, the wake harmonics.
Simple Riemannian surfaces are scattering rigid
Wen, Haomin
2015-01-01
Scattering rigidity of a Riemannian manifold allows one to tell the metric of a manifold with boundary by looking at the directions of geodesics at the boundary. Lens rigidity allows one to tell the metric of a manifold with boundary from the same information plus the length of geodesics. There are a variety of results about lens rigidity but very little is known for scattering rigidity. We will discuss the subtle difference between these two types of rigidities and prove that they are equiva...
Zestanakis, P A; Anastassiou, G; Hizanidis, K
2015-01-01
The presence of non-axisymmetric perturbations in an axisymmetric magnetic field equilibrium renders the Guiding Center (GC) particle motion non-integrable and may result in particle, energy and momentum redistribution, due to resonance mechanisms. We analyse these perturbations in terms of their spectrum, as observed by the particles in the frame of unperturbed GC motion. We calculate semi-analytically the exact locations and strength of resonant spectral components of multiple perturbations. The presented Orbital Spectrum Analysis (OSA) method is based on an exact Action-Angle transform that fully takes into account Finite Orbit Width (FOW) effects. The method provides insight into the particle dynamics and enables the prediction of the effect of any perturbation to all different types of particles and orbits in a given, analytically or numerically calculated, axisymmetric equilibrium.
Non-axisymmetric equilibrium reconstruction for stellarators, reversed field pinches and tokamaks
Energy Technology Data Exchange (ETDEWEB)
Hanson, James D. [Auburn University, Auburn, Alabama; Anderson, D.T. [University of Wisconsin, Madison; Cianciosa, M. [Auburn University, Auburn, Alabama; Franz, P. [EURATOM / ENEA, Italy; Harris, J. H. [Oak Ridge National Laboratory (ORNL); Hartwell, G. H. [Auburn University, Auburn, Alabama; Hirshman, Steven Paul [ORNL; Knowlton, Stephen F. [Auburn University, Auburn, Alabama; Lao, Lang L. [General Atomics, San Diego; Lazarus, Edward Alan [ORNL; Marrelli, L. [Association EURATOM ENEA Fusion, Consorzio RFX, Padua, Italy; Maurer, D. A. [Auburn University, Auburn, Alabama; Schmitt, J. C. [Princeton Plasma Physics Laboratory (PPPL); Sontag, A. C. [Oak Ridge National Laboratory (ORNL); Stevenson, B. A. [Auburn University, Auburn, Alabama; Terranova, D. [Association EURATOM ENEA Fusion, Consorzio RFX, Padua, Italy
2013-01-01
Axisymmetric equilibrium reconstruction using magnetohydrodynamic equilibrium solutions to the Grad Shafranov equation has long been an important tool for interpreting tokamak experiments. This paper describes recent results in non-axisymmetric (three-dimensional) equilibrium reconstruction of nominally axisymmetric plasmas (tokamaks and reversed field pinches (RFPs)), and fully non-axisymmetric plasmas (stellarators). Results from applying the V3FIT code to CTH and HSX stellarator plasmas, RFX-mod RFP plasmas and the DIII-D tokamak are presented.
Geometry, rigidity, and group actions
Farb, Benson; Zimmer, Robert J
2011-01-01
The study of group actions is more than a hundred years old but remains to this day a vibrant and widely studied topic in a variety of mathematic fields. A central development in the last fifty years is the phenomenon of rigidity, whereby one can classify actions of certain groups, such as lattices in semi-simple Lie groups. This provides a way to classify all possible symmetries of important spaces and all spaces admitting given symmetries. Paradigmatic results can be found in the seminal work of George Mostow, Gergory Margulis, and Robert J. Zimmer, among others.The p
Wage rigidity and job creation
Christian Haefke; Marcus Sonntag; Thijs van Rens
2007-01-01
Recent research in macroeconomics emphasizes the role of wage rigidity in accounting for the volatility of unemployment fluctuations. We use worker-level data from the CPS to measure the sensitivity of wages of newly hired workers to changes in aggregate labor market conditions. The wage of new hires, unlike the aggregate wage, is volatile and responds almost one-to-one to changes in labor productivity. We conclude that there is little evidence for wage stickiness in the data. We also show, h...
Wage Rigidity and Job Creation
Haefke, Christian; Sonntag, Marcus; Rens, Thijs van
2012-01-01
Recent research in macroeconomics emphasizes the role of wage rigidity in accounting for the volatility of unemployment fluctuations. We use worker-level data from the CPS to measure the sensitivity of wages of newly hired workers to changes in aggregate labor market conditions. The wage of new hires, unlike the aggregate wage, is volatile and responds almost one-to-one to changes in labor productivity. We conclude that there is little evidence for wage stickiness in the data. We also show, h...
Wage Rigidity and Job Creation
Christian Haefke; Marcus Sonntag; Thijs van Rens
2012-01-01
Recent research in macroeconomics emphasizes the role of wage rigidity in ac- counting for the volatility of unemployment fluctuations. We use worker-level data from the CPS to measure the sensitivity of wages of newly hired workers to changes in aggregate labor market conditions. The wage of new hires, unlike the aggregate wage, is volatile and responds almost one-to-one to changes in labor productivity. We conclude that there is little evidence for wage stickiness in the data. We also show,...
Computer program provides improved longitudinal response analysis for axisymmetric launch vehicles
Smith, W. W.; Walton, W. C., Jr.
1967-01-01
Computer program calculates axisymmetric launch vehicle steady-state response to axisymmetric sinusoidal loads. A finite element technique is utilized to construct the total launch vehicle stiffness matrix and mass matrix by subdividing the prototype structure into a set of axisymmetric shell components, fluid components, and spring-mass components.
Modelling axisymmetric cod-ends made of different mesh types
DEFF Research Database (Denmark)
Priour, D.; Herrmann, Bent; O'Neill, F.G.
2009-01-01
Cod-ends are the rearmost part of trawl fishing gears. They collect the catch, and for many important species it is where fish selection takes place. Generally speaking they are axisymmetric, and their shape is influenced by the catch volume, the mesh shape, and the material characteristics. The ...
Non-axisymmetric instabilities in discs with imposed zonal flows
Vanon, R.; Ogilvie, G. I.
2016-12-01
We conduct a linear stability calculation of an ideal Keplerian flow on which a sinusoidal zonal flow is imposed. The analysis uses the shearing sheet model and is carried out both in isothermal and adiabatic conditions, with and without self-gravity (SG). In the non-SG regime, a structure in the potential vorticity (PV) leads to a non-axisymmetric Kelvin-Helmholtz (KH) instability; in the short-wavelength limit its growth rate agrees with the incompressible calculation by Lithwick, which only considers perturbations elongated in the streamwise direction. The instability's strength is analysed as a function of the structure's properties, and zonal flows are found to be stable if their wavelength is ≳8 H, where H is the disc's scaleheight, regardless of the value of the adiabatic index γ. The non-axisymmetric KH instability can operate in Rayleigh-stable conditions, and it therefore represents the limiting factor to the structure's properties. Introducing SG triggers a second non-axisymmetric instability, which is found to be located around a PV maximum, while the KH instability is linked to a PV minimum, as expected. In the adiabatic regime, the same gravitational instability is detected even when the structure is present only in the entropy (not in the PV) and the instability spreads to weaker SG conditions as the entropy structure's amplitude is increased. This eventually yields a non-axisymmetric instability in the non-SG regime, albeit of weak strength, localized around an entropy maximum.
Stability of a compound sessile drop at the axisymmetric configuration.
Zhang, Ying; Chatain, Dominique; Anna, Shelley L; Garoff, Stephen
2016-01-15
The equilibrium configuration of compound sessile drops has been calculated previously in the absence of gravity. Using the Laplace equations, we establish seven dimensionless parameters describing the axisymmetric configuration in the presence of gravity. The equilibrium axisymmetric configuration can be either stable or unstable depending on the fluid properties. A stability criterion is established by calculating forces on a perturbed Laplacian shape. In the zero Bond number limit, the stability criterion depends on the density ratio, two ratios of interfacial tensions, the volume ratio of the two drops, and the contact angle. We use Surface Evolver to examine the stability of compound sessile drops at small and large Bond numbers and compare with the zero Bond number approximation. Experimentally, we realize a stable axisymmetric compound sessile drop in air, where the buoyancy force exerted by the air is negligible. Finally, using a pair of fluids in which the density ratio can be tuned nearly independently of the interfacial tensions, the stability transition is verified for the axisymmetric configuration. Even though the perturbations are different for the theory, simulations and experiments, both simulations and experiments agree closely with the zero Bond number approximation, exhibiting a small discrepancy at large Bond number.
Hawking radiation via tunnelling from general stationary axisymmetric black holes
Institute of Scientific and Technical Information of China (English)
Zhang Jing-Yi; Fan Jun-Hui
2007-01-01
Hawking radiation is viewed as a tunnelling process. In this way the emission rates of massless particles and massive particles tunnelling across the event horizon of general stationary axisymmetric black holes are calculated,separately. The emission spectra of these two different kinds of outgoing particles have the same functional form and both are consistent with an underlying unitary theory.
Fluid dynamics analysis of a rotating axisymmetric part using FIDAP
Giles, G. E.; Kirkpatrick, J. R.; Wendel, M. W.; Bullock, J. S., IV
1990-03-01
The effect of fluid flow on electrochemical plating on a rotating axisymmetric part was investigated by using a finite element computer code, FIDAP. The results from these investigations compare well with analytical results for laminar flow conditions. The addition of a nonrotating shield was also investigated for laminar flow conditions. An attempt to extend these analyses to turbulent conditions was unsuccessful.
Axisymmetric Consolidation of Unsaturated Soils by Differential Quadrature Method
Directory of Open Access Journals (Sweden)
Wan-Huan Zhou
2013-01-01
Full Text Available Axisymmetric consolidation in a sand drain foundation is a common problem in foundation engineering. In unsaturated soils, the excess pore-water and pore-air pressures simultaneously change during the consolidation procedure; and the solutions are not easy to obtain. The present paper uses the differential quadrature method (DQM for axisymmetric consolidation of unsaturated soils in a sand drain foundation. The radial seepage of sand drain foundation is considered based on the framework of Fredlund’s one-dimensional consolidation theory in unsaturated soils. With the use of Darcy’s law and Fick’s law, the polar governing equations of excess pore-air and pore-water pressures of axisymmetric consolidation are derived. By using DQM, the two governing equations are transformed into two sets of ordinary differential equations. Then the solutions of excess pore-water and pore-air pressures can be obtained by Rong-Kutta method. The DQM solution can be used to deal with the case of nonuniform initial pore-air and pore-water distributions. Finally, case studies are presented to investigate the behavior of axisymmetric consolidation of unsaturated soils. The convergence analysis and average degree of consolidation, the settlements in radial and vertical direction, and the effects of different initial excess pore pressure distributions are presented, and discussed in this paper.
ON INTEGRITY ASSESSMENT OF AXISYMMETRIC COMPONENTS OPERATING WITHIN CREEP REGIME
Institute of Scientific and Technical Information of China (English)
ZARRABI K; LAWRENCE Ng
2006-01-01
A multiaxial paradigm for predicting creep damage/lives of components is described. Although in principle the paradigm is general, it is verified using axisymmetric experimental data. It is shown that the proposed paradigm is capable of predicting creep lives with an error of less than 2%. It is also shown that the proposed paradigm is more accurate than the reference stress method.
Numerical computation of gravitational field for general axisymmetric objects
Fukushima, Toshio
2016-10-01
We developed a numerical method to compute the gravitational field of a general axisymmetric object. The method (i) numerically evaluates a double integral of the ring potential by the split quadrature method using the double exponential rules, and (ii) derives the acceleration vector by numerically differentiating the numerically integrated potential by Ridder's algorithm. Numerical comparison with the analytical solutions for a finite uniform spheroid and an infinitely extended object of the Miyamoto-Nagai density distribution confirmed the 13- and 11-digit accuracy of the potential and the acceleration vector computed by the method, respectively. By using the method, we present the gravitational potential contour map and/or the rotation curve of various axisymmetric objects: (i) finite uniform objects covering rhombic spindles and circular toroids, (ii) infinitely extended spheroids including Sérsic and Navarro-Frenk-White spheroids, and (iii) other axisymmetric objects such as an X/peanut-shaped object like NGC 128, a power-law disc with a central hole like the protoplanetary disc of TW Hya, and a tear-drop-shaped toroid like an axisymmetric equilibrium solution of plasma charge distribution in an International Thermonuclear Experimental Reactor-like tokamak. The method is directly applicable to the electrostatic field and will be easily extended for the magnetostatic field. The FORTRAN 90 programs of the new method and some test results are electronically available.
Stationary axisymmetric spacetimes with a conformally coupled scalar field
Astorino, Marco
2014-01-01
Solution generating techniques for general relativity with a conformally (and minimally) coupled scalar field are pushed forward to build a wide class of asymptotically flat, axisymmetric and stationary spacetimes continuously connected to Kerr. This family contains, amongst other things, rotating extensions of the BBMB black hole and also its angular and mass multipolar generalisations. Further addition of NUT charge is also discussed.
Decay of passive scalar fluctuations in axisymmetric turbulence
Yoshimatsu, Katsunori; Davidson, Peter A.; Kaneda, Yukio
2016-11-01
Passive scalar fluctuations in axisymmetric Saffman turbulence are examined theoretically and numerically. Theoretical predictions are verified by direct numerical simulation (DNS). According to the DNS, self-similar decay of the turbulence and the persistency of the large-scale anisotropy are found for its fully developed turbulence. The DNS confirms the time-independence of the Corrsin integral.
Unified characteristics line theory of spacial axisymmetric plastic problem
Institute of Scientific and Technical Information of China (English)
俞茂宏; 李建春; 张永强
2001-01-01
The unified strength theory proposed by Yu in 1991 is extended to spacial axisymmetric problem. A unified spacial axismymmetric characteristics line theory based on the unified strength theory is proposed. This theory takes account of different effects of intermediate principal stress on yielding or failure and the SD effect (tensile-compression strength difference) of materials. Various conventional axisymmetric characteristics line theories, whihc are based on the Haar-von Karman plastic condition, Szczepinski hypothesis, Tresca criterion, von Mises criterion and Mohr-Coulomb theory, are special cases of the new theory. Besides, a series of new spacial axisymmetric characteristics fields for different materials can be introduced. It forms a unified spacial axisymmetric characteristics theory. Two examples are calculated with the new theory, the results are compared with those obtained by the finite element program UEPP and those based on the Mohr-Coulomb strength theory. It is shown that the new theory is reliable and feasible. The economic benefit can be obtained from the engineering application of the new theory.
Non-Axisymmetric Shaping of Tokamaks Preserving Quasi-Axisymmetry
Energy Technology Data Exchange (ETDEWEB)
Long-Poe Ku and Allen H. Boozer
2009-06-05
If quasi-axisymmetry is preserved, non-axisymmetric shaping can be used to design tokamaks that do not require current drive, are resilient to disruptions, and have robust plasma stability without feedback. Suggestions for addressing the critical issues of tokamaks can only be validated when presented with sufficient specificity that validating experiments can be designed. The purpose of this paper is provide that specificity for non-axisymmetric shaping. To our knowledge, no other suggestions for the solution of a number of tokamak issues, such as disruptions, have reached this level of specificity. Sequences of three-field-period quasi-axisymmetric plasmas are studied. These sequences address the questions: (1) What can be achieved at various levels of non-axisymmetric shaping? (2) What simplifications to the coils can be achieved by going to a larger aspect ratio? (3) What range of shaping can be achieved in a single experimental facility? The sequences of plasmas found in this study provide a set of interesting and potentially important configurations.
PERIODIC MOTIONS OF SPINNING RIGID SPACECRAFT UNDER INFLUENCE OF GRAVITATIONAL AND MAGNETIC FIELDS
Institute of Scientific and Technical Information of China (English)
Yehia A. Abdel-aziz; M.H. Yehia; F. A. Abd El-Salam; M. Radwan
2006-01-01
The motion of a magnetized axisymmetric spacecraft about its center of mass in a circular orbit is considered, taking the gravitational and magnetic effects of the central body into account. Equations of motion of the reduced system are transformed to equations of plane motion of a charged particle under the action of electric and magnetic fields. Stationary motions of the system are determined and periodic motions near to them are constructed using the Lyapounoff theorem of the holomorphic integral.
Complications of rigid internal fixation.
Campbell, Chris A; Lin, Kant Y
2009-03-01
Over the past 20 years, there have been many advances in the development of bone fixation systems used in the practice of craniomaxillofacial surgery. As surgical practices have evolved, the complications of each technologic advance have changed accordingly. Interfragmentary instability of interosseous wiring has been replaced by the risk of exposure, infection, and palpability of plate and screw fixation systems. The improved rigidity of plate fixation requires anatomic alignment of fracture fragments. Failure to obtain proper alignment has led to the phenomenon known as "open internal fixation" of fracture fragments without proper reduction. The size of the plates has decreased to minimize palpability and exposure. However limitations in their application have been encountered due to the physiologic forces of the muscles of mastication and bone healing. In the pediatric population, the long-standing presence of plates in the cranial vault resulted in reports of transcranial migration and growth restriction. These findings led to the development of resorbable plating systems, which are associated with self-limited plate palpability and soft tissue inflammatory reactions. Any rigid system including these produces growth restriction in varying amounts. In this discussion, we review the reported complication rates of miniplating and microplating systems as well as absorptive plating systems in elective and traumatic craniofacial surgery.
Institute of Scientific and Technical Information of China (English)
顾国庆; 王开福; 许星
2012-01-01
基于刚体面内微小转动测量在实验力学测量中的必要性和重要性,开展了利用数字图像相关方法(DICM)定量测量转动角度和准确定位转动中心的研究.从理论上分析了刚体面内转动角度与面内位移分量之间的关系,运用计算机仿真散斑图进行数值模拟研究,得到的转动角度和转动中心位置测量误差都在2％以内,模拟结果验证了数字图像相关法进行刚体面内微小转动定量测量的可行性.运用数字图像相关法对刚体面内未知微小转动进行了实测,并与几何光学实验方法所得到的结果进行了比较,两者结果误差为3.1％,符合较好.实验结果表明数字图像相关方法可以作为定量测量刚体面内微小转动的有效方法.%Due to the necessity and importance of the measurement of in-plane micro-rotations of a rigid body in the field of experimental mechanics < an investigation of quantitative measurement of rotation angle and rotation-center location is developed with digital image correlation method (DICM). The relation between the rotation angle and the in-plane displacement components is analyzed through theoretical analysis. The study of numerical simulation is carried out by specklegram produced by computer simulation. The measurement errors of both rotation angle and rotation-center location are within 2%. It shows that digital image correlation method is quite competent for the quantitative measurement of in-plane micro-rotations. The unknown in-plane rotation of a rigid body is practically measured by using digital image correlation method. The obtained rotation angle is compared with the result obtained from the geometrical optics experiment. The relative error is 3. 1%. It shows that they are in good agreement. Experimental results indicate that digital image correlation method can be regarded as an efficient method to measure in-plane micro-rotations of a rigid body quantitatively.
Zhong, Shiyan; Spurzem, Rainer
2015-01-01
Tidal Disruption of stars by supermassive central black holes from dense rotating star clusters is modelled by high-accuracy direct N-body simulation. As in a previous paper on spherical star clusters we study the time evolution of the stellar tidal disruption rate and the origin of tidally disrupted stars, now according to several classes of orbits which only occur in axisymmetric systems (short axis tube and saucer). Compared with that in spherical systems, we found a higher TD rate in axisymmetric systems. The enhancement can be explained by an enlarged loss-cone in phase space which is raised from the fact that total angular momentum $\\bf J$ is not conserved. As in the case of spherical systems, the distribution of the last apocenter distance of tidally accreted stars peaks at the classical critical radius. However, the angular distribution of the origin of the accreted stars reveals interesting features. Inside the influence radius of the supermassive black hole the angular distribution of disrupted star...
ON THE COMMONALITY OF 10–30 AU SIZED AXISYMMETRIC DUST STRUCTURES IN PROTOPLANETARY DISKS
Energy Technology Data Exchange (ETDEWEB)
Zhang, Ke; Bergin, Edwin A.; Schwarz, Kamber R. [Department of Astronomy, University of Michigan, 1085 S. University Avenue, Ann Arbor, MI 48109 (United States); Blake, Geoffrey A. [Division of Geological and Planetary Sciences, California Institute of Technology, MC 150-21, Pasadena, CA 91125 (United States); Cleeves, L. Ilsedore [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States); Hogerheijde, Michiel; Salinas, Vachail, E-mail: kezhang@umich.edu [Leiden Observatory, Leiden University, P.O. Box 9513, 2300 RA Leiden (Netherlands)
2016-02-10
An unsolved problem in step-wise core-accretion planet formation is that rapid radial drift in gas-rich protoplanetary disks should drive millimeter-/meter-sized particles inward to the central star before large bodies can form. One promising solution is to confine solids within small-scale structures. Here, we investigate dust structures in the (sub)millimeter continuum emission of four disks (TW Hya, HL Tau, HD 163296, and DM Tau), a sample of disks with the highest spatial resolution Atacama Large Millimeter/submillimeter Array observations to date. We retrieve the surface brightness distributions using synthesized images and fitting visibilities with analytical functions. We find that the continuum emission of the four disks is ∼axisymmetric but rich in 10–30 AU-sized radial structures, possibly due to physical gaps, surface density enhancements, or localized dust opacity variations within the disks. These results suggest that small-scale axisymmetric dust structures are likely to be common, as a result of ubiquitous processes in disk evolution and planet formation. Compared with recent spatially resolved observations of CO snow lines in these same disks, all four systems show enhanced continuum emission from regions just beyond the CO condensation fronts, potentially suggesting a causal relationship between dust growth/trapping and snow lines.
On the Commonality of 10-30AU Sized Axisymmetric Dust Structures in Protoplanetary Disks
Zhang, Ke; Blake, Geoffrey A; Cleeves, L Ilsedore; Hogerheijde, Michiel; Salinas, Vachail; Schwarz, Kamber R
2016-01-01
An unsolved problem in step-wise core-accretion planet formation is that rapid radial drift in gas-rich protoplanetary disks should drive mm-/meter-sized particles inward to the central star before large bodies can form. One promising solution is to confine solids within small scale structures. Here we investigate dust structures in the (sub)mm continuum emission of four disks (TW Hya, HL Tau, HD 163296 and DM Tau), a sample of disks with the highest spatial resolution ALMA observations to date. We retrieve the surface brightness distributions using synthesized images and fitting visibilities with analytical functions. We find that the continuum emission of the four disks is ~axi-symmetric but rich in 10-30AU-sized radial structures, possibly due to physical gaps, surface density enhancements or localized dust opacity variations within the disks. These results suggest that small scale axi-symmetric dust structures are likely to be common, as a result of ubiquitous processes in disk evolution and planet format...
Axisymmetric Afterbody Test Case for CFD Validation
Disotell, Kevin; Rumsey, Christopher
2016-11-01
As simulation complexity increases, the corresponding need for systematic, high-fidelity validation data sets continues to be important to advance physics-based CFD models. To this end, a parametric body of revolution is proposed as an experimental platform to support a wide validation domain for turbulent boundary layers outside the current bounds of DNS. Recognizing the challenges of detailed flow exploration on complex 3-D geometries, an analytically-defined body of revolution is pursued as a tractable, state-of-the-art measurement case for complex turbulent flows having extra rates of strain. The central feature of the concept based upon work by Presz Jr. & Pitkin is an interchangeable afterbody which can be tailored to distort a turbulent boundary layer in various ways, with incoming properties controlled by the forebody. An introduction to the test case design and overview of recent progress focused on smooth-body, turbulent separation physics are presented. Supported by appointment to NASA Postdoctoral Program, administered by Universities Space Research Association.
FACTORS INFLUENCING BENDING RIGIDITY OF SUBMERGED VEGETATION
Institute of Scientific and Technical Information of China (English)
WU Long-hua; YANG Xiao-li
2011-01-01
The bending rigidity of submerged vegetation is closely related with vegetative drag force.This work aims at determining the effects of flow conditions and characteristics of vegetation on the bending rigidity of submerged vegetation.Based on the dimensional analysis method,the factors influencing the bending rigidity of individual submerged vegetation were analyzed.The relationship between the relative bending rigidity and its influencing factors was investigated by experimental observation,and a relative bending rigidity expression for submerged vegetation was obtained by means of multiple linear regression method.The results show that the submerged vegetation has three states under different inflow conditions,and the each critical relative bending rigidity of individual submerged vegetation was determined for the different states of submerged vegetation.
Rigid Ideals and Radicals of Ore Extensions
Institute of Scientific and Technical Information of China (English)
Chan Yong Hong; Tai Keun Kwak; S. Tariq Rizvi
2005-01-01
For an endomorphism σ of a ring R, Krempa called σ a rigid endomorphism if aσ(a) = 0 implies a= 0 for a ∈ R. A ring R is called rigid if there exists a rigid endomorphism of R. In this paper, we extend the σ-rigid property of a ring R to an ideal of R. For a σ-ideal Ⅰ of a ring R, we call Ⅰ a σ-rigid ideal if aσ(a) ∈Ⅰ implies a ∈Ⅰ for a ∈ R. We characterize σ-rigid ideals and study related properties. The connections of the prime radical and the upper nil radical of R with the prime radical and the upper nil radical of the Ore extension R[x; σ, δ], respectively, are also investigated.
Muggleton, J. M.; Rustighi, E.; Gao, Y.
2016-09-01
Waves that propagate at low frequencies in buried pipes are of considerable interest in a variety of practical scenarios, for example leak detection, remote pipe detection, and pipeline condition assessment and monitoring. Particularly useful are the n = 0, or axisymmetric, modes in which there is no displacement (or pressure) variation over the pipe cross section. Previous work has focused on two of the three axisymmetric wavetypes that can propagate: the s = 1, fluid- dominated wave; and the s = 2, shell-dominated wave. In this paper, the third axisymmetric wavetype, the s = 0 torsional wave, is studied. Whilst there is a large body of research devoted to the study of torsional waves and their use for defect detection in pipes at ultrasonic frequencies, little is known about their behaviour and possible exploitation at lower frequencies. Here, a low- frequency analytical dispersion relationship is derived for the torsional wavenumber for a buried pipe from which both the wavespeed and wave attenuation can be obtained. How the torsional waves subsequently radiate to the ground surface is then investigated, with analytical expressions being presented for the ground surface displacement above the pipe resulting from torsional wave motion within the pipe wall. Example results are presented and, finally, how such waves might be exploited in practice is discussed.
Rigidity and flexibility of biological networks
Gaspar, Merse E
2012-01-01
The network approach became a widely used tool to understand the behaviour of complex systems in the last decade. We start from a short description of structural rigidity theory. A detailed account on the combinatorial rigidity analysis of protein structures, as well as local flexibility measures of proteins and their applications in explaining allostery and thermostability is given. We also briefly discuss the network aspects of cytoskeletal tensegrity. Finally, we show the importance of the balance between functional flexibility and rigidity in protein-protein interaction, metabolic, gene regulatory and neuronal networks. Our summary raises the possibility that the concepts of flexibility and rigidity can be generalized to all networks.
Rigidizing Inflatable Deployable Dwelling (RIDD) Project
National Aeronautics and Space Administration — By combining thin thermoplastic films, woven Vectran reinforcements, and heat a reliable, deployable, rigidizing space habitat can be created. Although much research...
Experimental and numerical study on bubble-sphere interaction near a rigid wall
Li, S.; Zhang, A. M.; Han, R.; Liu, Y. Q.
2017-09-01
This study is concerned with the interaction between a violently oscillating bubble and a movable sphere with comparable size near a rigid wall, which is an essential physical phenomenon in many applications such as cavitation, underwater explosion, ultrasonic cleaning, and biomedical treatment. Experiments are performed in a cubic water tank, and the underwater electric discharge technique (580 V DC) is employed to generate a bubble that is initiated between a rigid wall and a sphere in an axisymmetric configuration. The bubble-sphere interactions are captured using a high-speed camera operating at 52 000 frames/s. A classification of the bubble-sphere interaction is proposed, i.e., "weak," "intermediate," and "strong" interactions, identified with three distinct bubble shapes at the maximum volume moment. In the numerical simulations, the boundary integral method and the auxiliary function method are combined to establish a full coupling model that decouples the mutual dependence between the force and the sphere motion. The main features of bubble dynamics in different experiments are well reproduced by our numerical model. Meanwhile, the pressure and velocity fields are also provided for clarifying the associated mechanisms. The effects of two dimensionless standoff parameters, namely, γs (defined as ds/Rm, where ds is the minimum distance between the initial bubble center and the sphere surface and Rm is the maximum bubble radius) and γw (defined as dw/Rm, where dw is the distance between the initial bubble center and the rigid wall), are also discussed.
Directory of Open Access Journals (Sweden)
Marcelo Alves Barros
2004-11-01
Full Text Available This work presents an investigation where some alternative conceptions are the origin and the processing of varied interpretations. As for that, it was proposed to high school students the resolution of certain problems that involved rigid bodies in constant rotation. These problems should be analysed within the perspective of the speed concept, which was previously known by the students, but abandoned by the explanations generated by the alternative conceptions.Este trabalho apresenta uma investigação em que algumas concepções alternativas são a origem e o desencadeamento de variadas interpretações. Para isso, foram propostos a alunos do ensino médio a resolução de determinados problemas que envolviam corpos rígidos em rotação constante. Estes problemas deveriam ser analisados dentro da perspectiva do conceito de velocidade, previamente conhecido dos alunos, mas abandonado pelas explicações geradas pelas concepções alternativas.
Institute of Scientific and Technical Information of China (English)
马龙; 王仕成; 闵海波; 郭扬
2016-01-01
本文研究了通信时延和联合连通切换拓扑条件下的多刚体系统分布式姿态一致性控制问题。通过构建有效的辅助向量并选择合适的Lyapunov-Krasovskii函数，分别对恒定通信时延和时变通信时延两种不同情况下的控制器进行了设计。数值仿真结果表明，本文提出的方法能够有效地解决这类分布式姿态一致性控制问题。%In this paper, we study the distributed attitude consensus problem for multiple networked rigid body systems in the case of communication time-delays together with jointly connected switching topologies. By constructing useful aux-iliary vectors and choosing proper common Lyapunov-Krasovskii functions, we design two control laws for two different cases respectively, i.e., the case with constant communication time-delays, and the case with time varying communication time-delays. Numerical simulation shows that the proposed algorithms are effective to this kind of distributed attitude consensus problem.
ANALYTIC EVALUATION OF RECTILINEARITY OF LOW RIGIDITY SHAFT DURING HARDENING PROCESS
Directory of Open Access Journals (Sweden)
Antoni Świć
2013-03-01
Full Text Available The essential influence of the unevenness of temperature distribution while heating in the technological process on dimensions stability of low rigidity elements was shown. The new approach was applied to formulate mathematical models, which describe the elastic and inelastic behaviour of piece using transfer functions and block diagrams, allowing to use frequency method for evaluation of the behaviour of dynamic semi-finished element as the rigid body.
A Convertible Spinal Orthosis for Controlled Torso Rigidity
Directory of Open Access Journals (Sweden)
Nicole I. Kern
2013-01-01
Full Text Available A traditional spinal orthosis in conjunction with a hip-knee-ankle-foot orthosis (HKAFO improves posture in persons with paraplegia during standing and walking. It also limits the wearer's range of motion when worn during other activities, such as vehicle transfer or sitting and reaching for objects. In order to regain full torso flexibility the user would need to remove the spinal orthosis which can be arduous and time consuming. A Convertible Spinal Orthosis (CSO that allows the user to switch between Locked rigid torso support and Unlocked free motion has been designed, fabricated and tested. It shows promise for increasing functionality, wear time and subject comfort. Analysis of movement has been performed with an able-bodied and a paraplegic subject wearing a rigid spinal orthosis, the CSO in both states, and without any bracing. Configuration state had the most impact on lateral bending. Mean values for the paraplegic subject of 27°, 38°, 48°, and 48° and for the able-bodied subject of 22°, 26°, 48°, and 45° were found for lateral bending of the upper torso relative to the thighs in the Rigid, Locked, Unlocked, and No-Brace states, respectively.
A comparison of neighbor search algorithms for large rigid molecules.
Artemova, Svetlana; Grudinin, Sergei; Redon, Stephane
2011-10-01
Fast determination of neighboring atoms is an essential step in molecular dynamics simulations or Monte Carlo computations, and there exists a variety of algorithms to efficiently compute neighbor lists. However, most of these algorithms are general, and not specifically designed for a given type of application. As a result, although their average performance is satisfactory, they might be inappropriate in some specific application domains. In this article, we study the case of detecting neighbors between large rigid molecules, which has applications in, e.g., rigid body molecular docking, Monte Carlo simulations of molecular self-assembly or diffusion, and rigid body molecular dynamics simulations. More precisely, we compare the traditional grid-based algorithm to a series of hierarchy-based algorithms that use bounding volumes to rapidly eliminate large groups of irrelevant pairs of atoms during the neighbor search. We compare the performance of these algorithms based on several parameters: the size of the molecules, the average distance between them, the cutoff distance, as well as the type of bounding volume used in the culling hierarchy (AABB, OBB, wrapped, or layered spheres). We demonstrate that for relatively large systems (> 100,000 atoms) the algorithm based on the hierarchy of wrapped spheres shows the best results and the traditional grid-based algorithm gives the worst timings. For small systems, however, the grid-based algorithm and the one based on the wrapped sphere hierarchy are beneficial. Copyright © 2011 Wiley Periodicals, Inc.
Axisymmetric instability in a noncircular tokamak: experiment and theory
Energy Technology Data Exchange (ETDEWEB)
Lipschultz, B.; Prager, S.C.; Todd, A.M.M.; Delucia, J.
1979-09-01
The stability of dee, inverse-dee and square cross section plasmas to axisymmetric modes has been investigated experimentally in Tokapole II, a tokamak with a four-null poloidal divertor. Experimental results are closely compared with predictions of two numerical stability codes -- the PEST code (ideal MHD, linear stability) adapted to tokapole geometry and a code which follows the nonlinear evolution of shapes similar to tokapole equilibria. Experimentally, the square is vertically stable and both dee's unstable to a vertical nonrigid axisymmetric shift. The central magnetic axis displacement grows exponentially with a growth time approximately 10/sup 3/ poloidal Alfven times plasma time. Proper initial positioning of the plasma on the midplane allows passive feedback to nonlinearly restore vertical motion to a small stable oscillation. Experimental poloidal flux plots are produced directly from internal magnetic probe measurements.
Stable photon orbits in stationary axisymmetric electrovacuum spacetimes
Dolan, Sam R.; Shipley, Jake O.
2016-08-01
We investigate the existence and phenomenology of stable photon orbits (SPOs) in stationary axisymmetric electrovacuum spacetimes in four dimensions. First, we review the classification of equatorial circular photon orbits on Kerr-Newman spacetimes in the charge-spin plane. Second, using a Hamiltonian formulation, we show that Reissner-Nordström diholes (a family encompassing the Majumdar-Papapetrou and Weyl-Bach special cases) admit SPOs, in a certain parameter regime that we investigate. Third, we explore the transition from order to chaos for typical SPOs bounded within a toroidal region around a dihole, via a selection of Poincaré sections. Finally, for general axisymmetric stationary spacetimes, we show that the Einstein-Maxwell field equations allow for the existence of SPOs in electro vacuum, but not in pure vacuum.
Thermodynamic Volume Product in Spherically Symmetric and Axisymmetric Spacetime
Pradhan, Parthapratim
2016-01-01
In this Letter, we compute particularly thermodynamic \\emph{volume product, volume sum, volume minus and volume division} for wide variety of spherically symmetric spacetime and axisymmetric spacetime in the frame work of \\emph{extended phase space}. We consider Einstein gravity as well as other than Einstein gravity i.e. \\emph{Ho\\v{r}ava Lifshitz} gravity. We speculate that for spherically symmetric black holes the volume product is mass-independent both in Einstein gravity as well as Ho\\v{r}ava Lifshitz gravity while the other combination is mass-dependent. For axisymmetric black hole spacetime in Einstein gravity all the combination is \\emph{mass-dependent}. There has been no chance to generate any combination of volume product is mass-independent. Interestingly, \\emph{only rotating BTZ black hole} in 3D provides the volume product formula is mass-independent i.e. \\emph{universal} and hence it is quantized.
Modeling the Orion nebula as an axisymmetric blister
Rubin, R. H.; Simpson, J. P.; Haas, M. R.; Erickson, E. F.
1991-01-01
The ionized gas in the Orion nebula is examined by means of axisymmetric modeling that is based on observational data from the ionized, neutral, and molecular regions. Nonsymmetrical features are omitted, radial dependence from the Trapezium is assumed, and azimuthal symmetry in the plane of the sky is used. Stellar properties and abundances of certain elements are described, and these data are used to compare the present axisymmetric-blister model to a previous spherical model. Strong singly-ionized emission that are visible near the Trapezium are found to originate in the ionization-bounded region in the dense Trapezium zone. The model can be more tightly constrained by adding near-IR data on noncentral zones for (Ar II), (AR III), (Ne II), and (S IV). The quadrant with the 'bar' creates an nonsymmetry that influences the observational data, and the model can therefore be improved with the additional data.
The axisymmetric jet in a rotating reference frame
Energy Technology Data Exchange (ETDEWEB)
Lawrie, A G W; Scott, J F; Godeferd, F; Cambon, C [LMFA, Ecole Centrale de Lyon (France); Duran-Matute, M; Flor, J-B [LEGI, Universite Joseph Fourier, Grenoble (France); Danaila, L, E-mail: andrew.lawrie@ec-lyon.fr [CORIA, Universite de Rouen (France)
2011-12-22
The axisymmetric jet is a geometrically simple, statistically stationary example of inhomogenous turbulence. Considering conservation of volume and momentum, Morton et al. (1956) offered a prediction of jet development, characterised solely by an unknown, constant entrainment coefficient. The presence of background rotation complicates the kinematics of the entrainment, and without special treatment, the jet suffers a helical instability. Here, we present one technique which stabilises the axisymmetric jet, yet preserves its desirable turbulent properties. The jet offers a steady-state flow in which there is an axial variation of local Rossby number, and after decay along the axis to a critical value, cones of inertial waves emerge. In this paper, we demonstrate these features using our numerical software MOBILE, offer our solution to stabilise the jet, and explain the mechanisms involved.
Mobility of an axisymmetric particle near an elastic interface
Daddi-Moussa-Ider, Abdallah; Gekle, Stephan
2016-01-01
Using a fully analytical theory, we compute the leading order corrections to the translational, rotational and translation-rotation coupling mobilities of an arbitrary axisymmetric particle immersed in a Newtonian fluid moving near an elastic cell membrane that exhibits resistance towards stretching and bending. The frequency-dependent mobility corrections are expressed as general relations involving separately the particle's shape-dependent bulk mobility and the shape-independent parameters such as the membrane-particle distance, the particle orientation and the characteristic frequencies associated with shearing and bending of the membrane. This makes the equations applicable to an arbitrary-shaped axisymmetric particle provided that its bulk mobilities are known, either analytically or numerically. For a spheroidal particle, these general relations reduce to simple expressions in terms of the particle's eccentricity. We find that the corrections to the translation-rotation coupling mobility are primarily d...
Dynamics and thermodynamics of axisymmetric flows: I. Theory
Leprovost, N; Chavanis, P H; Leprovost, Nicolas; Chavanis, Pierre-Henri
2005-01-01
We develop new variational principles to study stability and equilibrium of axisymmetric flows. We show that there is an infinite number of steady state solutions. We show that these steady states maximize a (non-universal) $H$-function. We derive relaxation equations which can be used as numerical algorithm to construct stable stationary solutions of axisymmetric flows. In a second part, we develop a thermodynamical approach to the equilibrium states at some fixed coarse-grained scale. We show that the resulting distribution can be divided in a universal part coming from the conservation of robust invariants and one non-universal determined by the initial conditions through the fragile invariants (for freely evolving systems) or by a prior distribution encoding non-ideal effects such as viscosity, small-scale forcing and dissipation (for forced systems). Finally, we derive a parameterization of inviscid mixing to describe the dynamics of the system at the coarse-grained scale.
On the galactic rotation curves problem within an axisymmetric approach
Alvarez, Cesar; Herrera-Aguilar, Alfredo; Nucamendi, Ulises; Santos, Eli
2013-01-01
In U. Nucamendi et al. Phys. Rev. D63 (2001) 125016 and K. Lake, Phys. Rev. Lett. 92 (2004) 051101 it has been shown that galactic potentials can be kinematically linked to the observed red/blue shifts of the corresponding galactic rotation curves under a minimal set of assumptions: the emitted photons come from stable timelike circular geodesic orbits of stars in a static spherically symmetric gravitational field, and propagate to us along null geodesics. It is remarkable that this relation can be established without appealing at all to a concrete theory of gravitational interaction. Here we generalize this kinematical spherically symmetric approach to the galactic rotation curves problem to the stationary axisymmetric realm since this is precisely the symmetry that spiral galaxies possess. Thus, by making use of the most general stationary axisymmetric metric, we also consider stable circular orbits of stars that emit signals which travel to a distant observer along null geodesics and express the galactic r...
A Non-axisymmetric Spherical α2-Dynamo
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Using the Chebyshev-tau method, the generation of oscillatory nonaxisymmetric stellar magnetic fields by the α2-dynamo is studied in spherical geometry. Following the boundary conditions given by Schubert & Zhang, the spherical α2-dynamo consists of a fully convective spherical shell with inner radius ri and outer radius ro. A comparison of the critical dynamo numbers of axisymmetric and φ-dependent modes for different thicknesses of the convective shell and different α-profiles leads to the following qualitative results: (I) when the angular factor of α-profile is sinnθ cosθ (n = 1, 2, 4) the solutions of the α2-dynamo are oscillatory and non-axisymmetric, (ii) the thinner the convective shell, the more easily is the nonaxisymmetric mode excited and the higher is the latitudinal wave number, (iii) the thickness of the outer convective shell has an effect on the symmetries of the magnetic fields.
Linear Stability of Hill's Vortex to Axisymmetric Perturbations
Protas, Bartosz
2015-01-01
We consider the linear stability of Hill's vortex with respect to axisymmetric perturbations. Given that Hill's vortex is a solution of a free-boundary problem, this stability analysis is performed by applying methods of shape differentiation to the contour dynamics formulation of the problem in a 3D axisymmetric geometry. This approach allows us to systematically account for the effect of boundary deformations on the linearized evolution of the vortex under the constraint of constant circulation. The resulting singular integro-differential operator defined on the vortex boundary is discretized with a highly accurate spectral approach. This operator has two unstable and two stable eigenvalues complemented by a continuous spectrum of neutrally-stable eigenvalues. By considering a family of suitably regularized (smoothed) eigenvalue problems solved with a range of numerical resolutions we demonstrate that the corresponding eigenfunctions are in fact singular objects in the form of infinitely sharp peaks localiz...
Non Axi-symmetric Anisotropy of Solar Wind Turbulence
Turner, A J; Chapman, S C; Hnat, B; Mueller, W -C
2011-01-01
A key prediction of turbulence theories is frame-invariance, and in magnetohydrodynamic (MHD) turbulence, axisymmetry of fluctuations with respect to the background magnetic field. Paradoxically the power in fluctuations in the turbulent solar wind are observed to be ordered with respect to the bulk macroscopic flow as well as the background magnetic field. Here, non- axisymmetry across the inertial and dissipation ranges is quantified using in-situ observations from Cluster. The observed inertial range non- axisymmetry is reproduced by a 'fly through' sampling of a Direct Numerical Simulation of MHD turbulence. Furthermore, 'fly through' sampling of a linear superposition of transverse waves with axisymmetric fluctuations generates the trend in non- axisymmetry with power spectral exponent. The observed non-axisymmetric anisotropy may thus simply arise as a sampling effect related to Taylor's hypothesis and is not related to the plasma dynamics itself.
Steady-State Axisymmetric MHD Solutions with Various Boundary Conditions
Wang, Lile
2014-01-01
Axisymmetric magnetohydrodynamics (MHD) can be invoked for describing astrophysical magnetized flows and formulated to model stellar magnetospheres including main sequence stars (e.g. the Sun), compact stellar objects [e.g. magnetic white dwarfs (MWDs), radio pulsars, anomalous X-ray pulsars (AXPs), magnetars, isolated neutron stars etc.], and planets as a major step forward towards a full three-dimensional model construction. Using powerful and reliable numerical solvers based on two distinct finite-difference method (FDM) and finite-element method (FEM) schemes of algorithm, we examine axisymmetric steady-state or stationary MHD models in Throumoulopoulos & Tasso (2001), finding that their separable semi-analytic nonlinear solutions are actually not unique given their specific selection of several free functionals and chosen boundary conditions. The multiplicity of nonlinear steady MHD solutions gives rise to differences in the total energies contained in the magnetic fields and flow velocity fields as ...
Grad-Shafranov Approach To Axisymmetric Stationary Flows In Astrophysics
Beskin, V S
2004-01-01
My lecture is devoted to the analytical results available for a large class of axisymmetric stationary flows in the vicinity of compact astrophysical objects. First, the most general case is formulated corresponding to the axisymmetric stationary MHD flow in the Kerr metric. Then, I discuss the hydrodynamical version of the Grad-Shafranov equation. Although not so well-known as the full MHD one, it allows us to clarify the nontrivial structure of the Grad-Shafranov approach as well as to discuss the simplest version of the 3+1-split language -- the most convenient one for the description of ideal flows in the vicinity of rotating black holes. Finally, I consider several examples that demonstrate how this approach can be used to obtain the quantitative description of the real transonic flows in the vicinity of rotating and moving black holes.
Stable photon orbits in stationary axisymmetric electrovacuum spacetimes
Dolan, Sam R
2016-01-01
We investigate the existence and phenomenology of stable photon orbits (SPOs) in stationary axisymmetric electrovacuum spacetimes in four dimensions. First, we classify the equatorial circular photon orbits of Kerr-Newman spacetimes in the charge-spin plane. Second, using a Hamiltonian formulation, we show that Reissner-Nordstr\\"om di-holes (a family encompassing the Majumdar-Papapetrou and Weyl-Bach special cases) admit SPOs, in a certain parameter regime that we investigate. Third, we explore the transition from order to chaos for typical SPOs bounded within a torus around a di-hole, via a selection of Poincar\\'e sections. Finally, for general axisymmetric stationary spacetimes, we show that the Einstein-Maxwell field equations allow for the existence of SPOs in electrovacuum; but not in pure vacuum.
Stability of the Shallow Axisymmetric Parabolic-Conic Bimetallic Shell by Nonlinear Theory
Directory of Open Access Journals (Sweden)
M. Jakomin
2011-01-01
Full Text Available In this contribution, we discuss the stress, deformation, and snap-through conditions of thin, axi-symmetric, shallow bimetallic shells of so-called parabolic-conic and plate-parabolic type shells loaded by thermal loading. According to the theory of the third order that takes into account the balance of forces on a deformed body, we present a model with a mathematical description of the system geometry, displacements, stress, and thermoelastic deformations. The equations are based on the large displacements theory. We numerically calculate the deformation curve and the snap-through temperature using the fourth-order Runge-Kutta method and a nonlinear shooting method. We show how the temperature of both snap-through depends on the point where one type of the rotational curve transforms into another.
Experimental study of libration-driven zonal flows in non-axisymmetric containers
Noir, Jerome; Bars, Michael Le; Sauret, Alban; Aurnou, J M; 10.1016/j.pepi.2012.05.005
2013-01-01
Orbital dynamics that lead to longitudinal libration of celestial bodies also result in an elliptically deformed equatorial core-mantle boundary. The non-axisymmetry of the boundary leads to a topographic coupling between the assumed rigidmantle and the underlying low viscosity fluid.The present experimental study investigates theeffect of non axisymmetric boundaries on the zonal flow driven by longitudinal libration. For large enough equatorial ellipticity, we report intermittent space-filling turbulence in particular bands of resonant frequency correlated with larger amplitude zonal flow. The mechanism underlying the intermittent turbulence has yet to be unambiguously determined. Nevertheless, recent numerical simulations in triaxial and biaxial ellipsoids suggest that it may be associated with the growth and collapse of an elliptical instability (Cebron et al., 2012). Outside of the band of resonance, we find that the background flow is laminar and the zonal flow becomes independent of the geometry at firs...
Ballistics Modeling for Non-Axisymmetric Hypervelocity Smart Bullets
2014-06-03
1DoD PETTT, Dynamics Research Corporation, Andover, MA; on-site at NRL. Railgun 67-6754-04 Ballistics Modeling for non-Axisymmetric Hypervelocity...report is concerned with calculating the trajectory of the projectile fired from an electromagnetic launcher, or railgun , which attains supersonic...at supersonic speeds [1]. In the case of a railgun , there is no requirement involving a casing or high pressure seal. Instead, there is a requirement
Some more Non-arithmetic Rigid groups
Lubotzky, Alexander
2011-01-01
In "Non arithmetic super rigid groups: counter examples to Platonov's conjecture" Bass and Lubotzky gave a counter example to Platonov's conjecture by presenting an example of a linear group with super-rigidity which is not an arithmetic lattice. In this note, a much richer class of such groups is presented with a somewhat simpler proof.
Three-Dimensional Electromagnetic High Frequency Axisymmetric Cavity Scars.
Energy Technology Data Exchange (ETDEWEB)
Warne, Larry Kevin; Jorgenson, Roy Eberhardt
2014-10-01
This report examines the localization of high frequency electromagnetic fi elds in three-dimensional axisymmetric cavities along periodic paths between opposing sides of the cavity. The cases where these orbits lead to unstable localized modes are known as scars. This report treats both the case where the opposing sides, or mirrors, are convex, where there are no interior foci, and the case where they are concave, leading to interior foci. The scalar problem is treated fi rst but the approximations required to treat the vector fi eld components are also examined. Particular att ention is focused on the normalization through the electromagnetic energy theorem. Both projections of the fi eld along the scarred orbit as well as point statistics are examined. Statistical comparisons are m ade with a numerical calculation of the scars run with an axisymmetric simulation. This axisymmetric cas eformstheoppositeextreme(wherethetwomirror radii at each end of the ray orbit are equal) from the two -dimensional solution examined previously (where one mirror radius is vastly di ff erent from the other). The enhancement of the fi eldontheorbitaxiscanbe larger here than in the two-dimensional case. Intentionally Left Blank
Stability of perturbed geodesics in $nD$ axisymmetric spacetimes
Coimbra-Araujo, C H
2016-01-01
The effect of self-gravity of a disk matter is evaluated by the simplest modes of oscillation frequencies for perturbed circular geodesics. It is plotted the radial profiles of free oscillations of an equatorial circular geodesic perturbed within the orbital plane or in the vertical direction. The calculation is carried out to geodesics of an axisymmetric $n$-dimensional spacetime. The profiles are computed by examples of disks embeded in five-dimensional or six-dimensional spacetime, where it is studied the motion of free test particles for three axisymmetric cases: (i) the Newtonian limit of a general proposed $5D$ and $6D$ axisymmetric spacetime; (ii) a simple Randall-Sundrum $5D$ spacetime; (iii) general $5D$ and $6D$ Randall-Sundrum spacetime. The equation of motion of such particles is derived and the stability study is computed for both horizontal and vertical directions, to see how extra dimensions could affect the system. In particular, we investigate a disk constructed from Schwarzschild and Chazy-C...
Are better conductors more rigid?
Eom, Young-Ho; Jeong, Hawoong; Orland, Henri; Yi, Juyeon
2006-10-01
The variation of the bending stiffness of various materials is studied from the point of view of the electronic band characteristics. As far as the electronically generated bending stiffness κe (which we refer to as electro-stiffness) is concerned, the relevant factors are the orbital overlap t, the gap width u between the valence band and the conduction band, and the electron filling fraction γ. A perturbative calculation leads to the approximate expression κe ~ t2/√u2 + t2. This shows that materials with a large overlap and narrow band gap should be stiffer. The electro-stiffness also depends on the electron filling-fraction. We find that κe(γ) <= κe(1/2). These kinds of behavior are confirmed by numerical calculations. In addition, we study the variation in the projected length of flexible molecules under a voltage bias. The nonlinear variation of the bending rigidity is shown to give rise to a length contraction or dilation, depending on the voltage bias.
Reorientation of Asymmetric Rigid Body Using Two Controls
Directory of Open Access Journals (Sweden)
Donghoon Kim
2013-01-01
Full Text Available Most spacecrafts are designed to be maneuvered to achieve pointing goals. This is accomplished usually by designing a three-axis control system, which can achieve arbitrary maneuvers, where the goal is to repoint the spacecraft and match a desired angular velocity at the end of the maneuver. New control laws are required, however, if one of the three-axis control actuators fails. This paper explores suboptimal maneuver strategies when only two control torque inputs are available. To handle this underactuated system control problem, the three-axis maneuver strategy is transformed to two successive independent submaneuver strategies. The first maneuver is conducted on one of the available torque axes. Next, the second maneuver is conducted on the torque available plane using two available control torques. However, the resulting control law is more complicated than the general three-axis control law. This is because an optimal switch time needs to be found for determining the end time for the single-axis maneuver or the start time for the second maneuver. Numerical simulation results are presented that compare optimal maneuver strategies for both nominal and failed actuator cases.
Euler-Poincaré Reduction of a Rigid Body Motion
DEFF Research Database (Denmark)
Wisniewski, Rafal; Kulczycki, P.
2004-01-01
. Assuming that the system possesses symmetry and the configuration manifold corresponds to a Lie group, the Euler-Poincaré reduction breaks up the motion into separate equations of dynamics and kinematics. This becomes of particular interest for modelling, estimation and control of mechanical systems...
Reduced Order Aeroservoelastic Models with Rigid Body Modes Project
National Aeronautics and Space Administration — Complex aeroelastic and aeroservoelastic phenomena can be modeled on complete aircraft configurations generating models with millions of degrees of freedom. Starting...
Fractional-order theory of heat transport in rigid bodies
Zingales, Massimiliano
2014-11-01
The non-local model of heat transfer, used to describe the deviations of the temperature field from the well-known prediction of Fourier/Cattaneo models experienced in complex media, is framed in the context of fractional-order calculus. It has been assumed (Borino et al., 2011 [53], Mongioví and Zingales, 2013 [54]) that thermal energy transport is due to two phenomena: (i) A short-range heat flux ruled by a local transport equation; (ii) A long-range thermal energy transfer proportional to a distance-decaying function, to the relative temperature and to the product of the interacting masses. The distance-decaying function is assumed in the functional class of the power-law decay of the distance yielding a novel temperature equation in terms of α-order Marchaud fractional-order derivative (0⩽α⩽1). Thermodynamical consistency of the model is provided in the context of Clausius-Plank inequality. The effects induced by the boundary conditions on the temperature field are investigated for diffusive as well as ballistic local heat flux. Deviations of the temperature field from the linear distributions in the neighborhood of the thermostated zones of small-scale conductors are qualitatively predicted by the used fractional-order heat transport model, as shown by means of molecular dynamics simulations.
Hamiltonian Dynamics of Spider-Type Multirotor Rigid Bodies Systems
Doroshin, Anton V.
2010-03-01
This paper sets out to develop a spider-type multiple-rotor system which can be used for attitude control of spacecraft. The multirotor system contains a large number of rotor-equipped rays, so it was called a ``Spider-type System,'' also it can be called ``Rotary Hedgehog.'' These systems allow using spinups and captures of conjugate rotors to perform compound attitude motion of spacecraft. The paper describes a new method of spacecraft attitude reorientation and new mathematical model of motion in Hamilton form. Hamiltonian dynamics of the system is investigated with the help of Andoyer-Deprit canonical variables. These variables allow obtaining exact solution for hetero- and homoclinic orbits in phase space of the system motion, which are very important for qualitative analysis.
Efficiency of Wave-Driven Rigid Body Rotation Toroidal Confinement
Rax, J -M; Fisch, N J
2016-01-01
The compensation of vertical drifts in toroidal magnetic fields through a wave-driven poloidal rotation is compared to compensation through the wave driven toroidal current generation to support the classical magnetic rotational transform. The advantages and drawbacks associated with the sustainment of a radial electric field are compared with those associated with the sustainment of a poloidal magnetic field both in terms of energy content and power dissipation. The energy content of a radial electric field is found to be smaller than the energy content of a poloidal magnetic field for a similar set of orbits. The wave driven radial electric field generation efficiency is similarly shown, at least in the limit of large aspect ratio, to be larger than the efficiency of wave-driven toroidal current generation.
GPU-based discrete element rigid body transport
CSIR Research Space (South Africa)
Govender, Nicolin
2013-08-01
Full Text Available The protection of harbours and coastal infrastructure is of vital importance to South Africa. A major development in the design of packing strategies for breakwaters is numerical modelling, and the use of physics engines and DEM models...
Quaternion Feedback Control for Rigid-body Spacecraft
DEFF Research Database (Denmark)
Jensen, Hans-Christian Becker; Wisniewski, Rafal
2001-01-01
This paper addresses three-axis attitude control for a Danish spacecraft, Roemer. The algorithm proposed is based on an approximation of the exact feedback linearisation for quaternionic attitude representation. The proposed attitude controller is tested in a simulation study. The environmental d...
Quaternion Feedback Control for Rigid-body Spacecraft
DEFF Research Database (Denmark)
Jensen, Hans-Christian Becker; Wisniewski, Rafal
2001-01-01
This paper addresses three-axis attitude control for a Danish spacecraft, Roemer. The algorithm proposed is based on an approximation of the exact feedback linearisation for quaternionic attitude representation. The proposed attitude controller is tested in a simulation study. The environmental d...... disturbances correspond to those expected for the Roemer mission. The pros and cons of the algorithm are discussed. The results of the study show that the controller is a > successful candidate for on-board implementation...
MUTUAL INFORMATION BASED 3D NON-RIGID REGISTRATION OF CT/MR ABDOMEN IMAGES
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
A mutual information based 3D non-rigid registration approach was proposed for the registration of deformable CT/MR body abdomen images. The Parzen Windows Density Estimation (PWDE) method is adopted to calculate the mutual information between the two modals of CT and MRI abdomen images. By maximizing MI between the CT and MR volume images, the overlapping part of them reaches the biggest, which means that the two body images of CT and MR matches best to each other. Visible Human Project (VHP) Male abdomen CT and MRI Data are used as experimental data sets. The experimental results indicate that this approach of non-rigid 3D registration of CT/MR body abdominal images can be achieved effectively and automatically, without any prior processing procedures such as segmentation and feature extraction, but has a main drawback of very long computation time. Key words: medical image registration; multi-modality; mutual information; non-rigid; Parzen window density estimation
Algorithms for Graph Rigidity and Scene Analysis
DEFF Research Database (Denmark)
Berg, Alex Rune; Jordán, Tibor
2003-01-01
We investigate algorithmic questions and structural problems concerning graph families defined by `edge-counts'. Motivated by recent developments in the unique realization problem of graphs, we give an efficient algorithm to compute the rigid, redundantly rigid, M-connected, and globally rigid...... by showing that 2d-connected bipartite graphs are d-tight. We give a new algorithm for finding a maximal d-sharp subgraph. We also answer a question of Imai and show that finding a maximum size d-sharp subgraph is NP-hard....
Institute of Scientific and Technical Information of China (English)
姜兴长; 杨方; 葛文杰; 杨静
2011-01-01
根据袋鼠的生物结构及跳跃的特点，建立了具有尾巴和脚趾的仿袋鼠跳跃机器人六刚体模型。应用拉格朗日方法，建立了机构在着地阶段的运动学和动力学方程。运用Matlab7．0对机器人进行仿真计算分析，给出了机器人在着地阶段的各关节转角、关节驱动力矩、质心轨迹、着地压力和ZMP随时间的变化规律。仿真结果表明：考虑尾巴的六刚体仿袋鼠跳跃机器人能显著提高机构的落地稳定性。%Bsaed on the bionic structure and the motion feature of a kangaroo, we estamlsn a mouel ior unlpeu hopping mechanism of a six-rigid-body bionic kangaroo with tail and toe. We adopt Lagrange method to establish the dynamics and kinematics equations for its stance phase. Taking the hopping robot with parameters as an example and using Matlab 7.0 for simulation ,we obtain the changing rule of each joint angle ,joint driving torque, the centroid trajectory, the ground pressure and ZMP with time of the stance phase. The result shows that the tail can greatly improve the stance stability of the bionic kangaroo robot.
On the Existence and Utility of Rigid Quasilocal Frames
Epp, Richard J; McGrath, Paul L
2013-01-01
The notion of a rigid quasilocal frame (RQF) provides a geometrically natural way to define a system in general relativity, and a new way to analyze the problem of motion. An RQF is defined as a two-parameter family of timelike worldlines comprising the boundary (topologically R x S^2) of the history of a finite spatial volume, with the rigidity conditions that the congruence of worldlines be expansion- and shear-free. In other words, the size and shape of the system do not change. In previous work, such systems in Minkowski space were shown to admit precisely the same six degrees of freedom of rigid body motion that we are familiar with in Newtonian space-time, without any constraints, circumventing a century-old theorem due to Herglotz and Noether. This is a consequence of the fact that a two-sphere of any shape always admits precisely six conformal Killing vector fields, which generate an action of the Lorentz group on the sphere. Here we review the previous work in flat spacetime and extend it in three di...
Coarse-grained rigid blob model for soft matter simulations
Chao, Sheng D.; Kress, Joel D.; Redondo, Antonio
2005-06-01
We have developed a coarse-grained multiscale molecular simulation method for soft matter systems that directly incorporates stereochemical information. We divide the material into disjoint groups of atoms or particles that move as separate rigid bodies; we call these groups "rigid blobs," hence the name coarse-grained rigid blob model. The method is enabled by the construction of transferable interblob potentials that approximate the net intermolecular interactions, as obtained from ab initio electronic structure calculations, other all-atom empirical potentials, experimental data, or any combination of the above. We utilize a multipolar expansion to obtain the interblob potential-energy functions. The series, which contains controllable approximations that allow us to estimate the errors, approaches the original intermolecular potential as the number of terms increases. Using a novel numerical algorithm, we can calculate the interblob potentials very efficiently in terms of a few interaction moment tensors. This reduces the labor well beyond what is required in standard molecular-dynamics calculations and allows large-scale simulations for temporal scales commensurate with characteristic times of nano- and mesoscale systems. A detailed derivation of the formulas is presented, followed by illustrative applications to several systems showing that the method can effectively capture realistic microscopic details and can easily extend to large-scale simulations.
Crack identification for rigid pavements using unmanned aerial vehicles
Bahaddin Ersoz, Ahmet; Pekcan, Onur; Teke, Turker
2017-09-01
Pavement condition assessment is an essential piece of modern pavement management systems as rehabilitation strategies are planned based upon its outcomes. For proper evaluation of existing pavements, they must be continuously and effectively monitored using practical means. Conventionally, truck-based pavement monitoring systems have been in-use in assessing the remaining life of in-service pavements. Although such systems produce accurate results, their use can be expensive and data processing can be time consuming, which make them infeasible considering the demand for quick pavement evaluation. To overcome such problems, Unmanned Aerial Vehicles (UAVs) can be used as an alternative as they are relatively cheaper and easier-to-use. In this study, we propose a UAV based pavement crack identification system for monitoring rigid pavements’ existing conditions. The system consists of recently introduced image processing algorithms used together with conventional machine learning techniques, both of which are used to perform detection of cracks on rigid pavements’ surface and their classification. Through image processing, the distinct features of labelled crack bodies are first obtained from the UAV based images and then used for training of a Support Vector Machine (SVM) model. The performance of the developed SVM model was assessed with a field study performed along a rigid pavement exposed to low traffic and serious temperature changes. Available cracks were classified using the UAV based system and obtained results indicate it ensures a good alternative solution for pavement monitoring applications.
Tidal Evolution of Asteroidal Binaries. Ruled by Viscosity. Ignorant of Rigidity
Efroimsky, Michael
2015-01-01
The rate of tidal evolution of asteroidal binaries is defined by the dynamical Love numbers divided by quality factors. Common is the (often illegitimate) approximation of the dynamical Love numbers with their static counterparts. As the static Love numbers are, approximately, proportional to the inverse rigidity, this renders a popular fallacy that the tidal evolution rate is determined by the product of the rigidity by the quality factor: $\\,k_l/Q\\propto 1/(\\mu Q)\\,$. In reality, the dynamical Love numbers depend on the tidal frequency and all rheological parameters of the tidally perturbed body (not just rigidity). We demonstrate that in asteroidal binaries the rigidity of their components plays virtually no role in tidal friction and tidal lagging, and thereby has almost no influence on the intensity of tidal interactions (tidal torques, tidal dissipation, tidally induced changes of the orbit). A key quantity that determines the tidal evolution is a product of the effective viscosity $\\,\\eta\\,$ by the tid...
Directory of Open Access Journals (Sweden)
Ferry Kwakkel
2011-12-01
Full Text Available Given a closed Riemannian manifold (M, g, i.e. compact and boundaryless, there is a partition of its tangent bundle TM = ∪iΣi called the focal decomposition of TM. The sets Σi are closely associated to focusing of geodesics of (M, g, i.e. to the situation where there are exactly i geodesic arcs of the same length joining points p and q in M. In this note, we study the topological structure of the focal decomposition of a closed Riemannian manifold and its relation with the metric structure of the manifold. Our main result is that flat n-tori, n > 2, are focally rigid in the sense that if two flat tori are focally equivalent then the tori are isometric up to rescaling. The case n = 2 was considered before by F. Kwakkel.Dada uma variedade Riemanniana (M, g fechada, isto é, compacta e sem bordo, existe uma partição de seu fibrado tangente TM = ∪iΣi chamada decomposição focal de TM. Os conjuntos Σi estão intimamente associados ao modo como focalizam as geodésicas de (M,g, isto é, à situação em que existem exatamente i arcos de geodésica de mesmo comprimento unindo pontos p e q em M. Nesta nota, estudamos a estrutura topológica da decomposição focal de uma variedade Riemanniana fechada e sua relação com a estrutura métrica de M. Nosso principal resultado é que n-toros planos, n > 2, são focalmente rigidos, isto é, se dois toros planos são focalmente equivalentes, então os dois toros são isométricos módulo mudança de escala. O caso n = 2 foi considerado anteriormente por F. Kwakkel.
van Driel, Martin; Nissen-Meyer, Tarje; Stähler, Simon; Waszek, Lauren; Hempel, Stefanie; Auer, Ludwig; Deuss, Arwen
2014-05-01
We present a numerical method to compute high-frequency 3D elastic waves in fully anisotropic axisymmetric media. The method is based on a decomposition of the wavefield into a series of uncoupled 2D equations, for which the dependence of the wavefield on the azimuth can be solved analytically. The remaining 2D problems are then solved using a spectral element method (AxiSEM). AxiSEM was recently published open-source (Nissen-Meyer et al. 2014) as a production ready code capable to compute global seismic wave propagation up to frequencies of ~2Hz. It accurately models visco-elastic dissipation and anisotropy (van Driel et al., submitted to GJI) and runs efficiently on HPC resources using up to 10K cores. At very short period, the Fresnel Zone of body waves is narrow and sensitivity is focused around the geometrical ray. In cases where the azimuthal variations of structural heterogeneity exhibit long spatial wavelengths, so called 2.5D simulations (3D wavefields in 2D models) provide a good approximation. In AxiSEM, twodimensional variations in the source-receiver plane are effectively modelled as ringlike structures extending in the out-of-plane direction. In contrast to ray-theory, which is widely used in high-frequency applications, AxiSEM provides complete waveforms, thus giving access to frequency dependency, amplitude variations, and peculiar wave effects such as diffraction and caustics. Here we focus on the practical implications of the inherent axisymmetric geometry and show how the 2.5D-features of our method method can be used to model realistic anisotropic structures, by applying it to problems such as the D" region and the inner core.
Effect of the free surface and the rigid plane on structural vibration and acoustic radiation
Institute of Scientific and Technical Information of China (English)
ZOU Yuanjie; ZHAO Deyou; LI Sheng
2004-01-01
The coupled fluid-structure interaction equation is established for bodies in the haft-space fluid domain, especially sitting on the infinite plane, based on the BEM (Boundary Element Method) theory. Then, the natural frequencies, vibration responses and the acoustic radiation for a box are calculated, and the effect of the free surface and the rigid plane is discussed. Finally, several relative factors including the plate thickness, the structure damping and the distance between the body and the infinite plane are studied. The results show that the effect of the free surface and the rigid plane on the structural natural frequencies, vibration responses and the acoustic radiation cannot be ignored.
Analysis of Switched-Rigid Floating Oscillator
Directory of Open Access Journals (Sweden)
Prabhakar R. Marur
2009-01-01
Full Text Available In explicit finite element simulations, a technique called deformable-to-rigid (D2R switching is used routinely to reduce the computation time. Using the D2R option, the deformable parts in the model can be switched to rigid and reverted back to deformable when needed during the analysis. The time of activation of D2R however influences the overall dynamics of the system being analyzed. In this paper, a theoretical basis for the selection of time of rigid switching based on system energy is established. A floating oscillator problem is investigated for this purpose and closed-form analytical expressions are derived for different phases in rigid switching. The analytical expressions are validated by comparing the theoretical results with numerical computations.
Roof-crush strength improvement using rigid polyurethane foam
Lilley, K.; Mani, A.
1998-08-01
Recent bending tests show the effectiveness of rigid, polyurethane foam in improving the strength of automotive body structures. By using foam, it is possible to reduce pillar sections, and to reduce thicknesses or eliminate reinforcements inside the pillars, and thereby offset the mass increase due to the foam filling. Further tests showed that utilizing the foam filling in a B-pillar to reduce section size can save ~20 mm that could be utilized to add energy absorbing structures in order to meet the new interior head impact requirements specified by the federal motor vehicle safety standards (FMVSS) 201 Head Impact Protection upgrade.
Stability of perturbed geodesics in nD axisymmetric spacetimes
Coimbra-Araújo, C. H.; Anjos, R. C.
2016-09-01
The effect of self-gravity of a disk matter is evaluated by the simplest modes of oscillation frequencies for perturbed circular geodesics. We plotted the radial profiles of free oscillations of an equatorial circular geodesic perturbed within the orbital plane or in the vertical direction. The calculation is carried out to geodesics of an axisymmetric n-dimensional spacetime. The profiles are computed by examples of disks embeded in five-dimensional or six-dimensional spacetime, where we studied the motion of free test particles for three axisymmetric cases: (i) the Newtonian limit of a general proposed 5D and 6D axisymmetric spacetime; (ii) a simple Randall-Sundrum (RS) 5D spacetime; (iii) general 5D and 6D RS spacetime. The equation of motion of such particles is derived and the stability study is computed for both horizontal and vertical directions, to see how extra dimensions could affect the system. In particular, we investigate a disk constructed from Miyamoto-Nagai and Chazy-Curzon with a cut parameter to generate a disk potential. Those solutions have a simple extension for extra dimensions in case (i), and by solving vacuum Einstein field equations for a kind of RS-Weyl metric in cases (ii) and (iii). We find that it is possible to compute a range of possible solutions where such perturbed geodesics are stable. Basically, the stable solutions appear, for the radial direction, in special cases when the system has 5D and in all cases when the system has 6D and, for the axial direction, in all cases when the system has both 5D or 6D.
Constants of motion in stationary axisymmetric gravitational fields
Markakis, C.
2014-07-01
The motion of test particles in stationary axisymmetric gravitational fields is generally non-integrable unless a non-trivial constant of motion, in addition to energy and angular momentum along the symmetry axis, exists. The Carter constant in Kerr-de Sitter space-time is the only example known to date. Proposed astrophysical tests of the black hole no-hair theorem have often involved integrable gravitational fields more general than the Kerr family, but the existence of such fields has been a matter of debate. To elucidate this problem, we treat its Newtonian analogue by systematically searching for non-trivial constants of motion polynomial in the momenta and obtain two theorems. First, solving a set of quadratic integrability conditions, we establish the existence and uniqueness of the family of stationary axisymmetric potentials admitting a quadratic constant. As in Kerr-de Sitter space-time, the mass moments of this class satisfy a `no-hair' recursion relation M2l +2 = a2M2l, and the constant is Noether related to a second-order Killing-Stäckel tensor. Second, solving a new set of quartic integrability conditions, we establish non-existence of quartic constants. Remarkably, a subset of these conditions is satisfied when the mass moments obey a generalized `no-hair' recursion relation M2l +4 = (a2 + b2)M2l +2 - a2b2M2l. The full set of quartic integrability conditions, however, cannot be satisfied non-trivially by any stationary axisymmetric vacuum potential.
Public policies targeting labour market rigidities
Andreea Claudia ŞERBAN
2013-01-01
Labour market rigidity becomes an issue of increasing importance under conditions of shocks associated with the economic crisis due to the need to increase the adaptability and responsiveness to them. Thus, labour market policies must be directed towards mitigating rigidities caused by institutional or demographic factors or certain mismatch between demand and supply of education qualifications. This paper highlights the major role of the active labour market policies tar...
A high-precision algorithm for axisymmetric flow
Directory of Open Access Journals (Sweden)
A. Gokhman
1995-01-01
Full Text Available We present a new algorithm for highly accurate computation of axisymmetric potential flow. The principal feature of the algorithm is the use of orthogonal curvilinear coordinates. These coordinates are used to write down the equations and to specify quadrilateral elements following the boundary. In particular, boundary conditions for the Stokes' stream-function are satisfied exactly. The velocity field is determined by differentiating the stream-function. We avoid the use of quadratures in the evaluation of Galerkin integrals, and instead use splining of the boundaries of elements to take the double integrals of the shape functions in closed form. This is very accurate and not time consuming.
Accuracy Improvement in Magnetic Field Modeling for an Axisymmetric Electromagnet
Ilin, Andrew V.; Chang-Diaz, Franklin R.; Gurieva, Yana L.; Il,in, Valery P.
2000-01-01
This paper examines the accuracy and calculation speed for the magnetic field computation in an axisymmetric electromagnet. Different numerical techniques, based on an adaptive nonuniform grid, high order finite difference approximations, and semi-analitical calculation of boundary conditions are considered. These techniques are being applied to the modeling of the Variable Specific Impulse Magnetoplasma Rocket. For high-accuracy calculations, a fourth-order scheme offers dramatic advantages over a second order scheme. For complex physical configurations of interest in plasma propulsion, a second-order scheme with nonuniform mesh gives the best results. Also, the relative advantages of various methods are described when the speed of computation is an important consideration.
Axisymmetric Natural Frequencies of Statically Loaded Annular Plates
Directory of Open Access Journals (Sweden)
Eihab M. Abdel-Rahman
2003-01-01
Full Text Available We present a numerical procedure to solve the axisymmetric vibration problem of statically loaded annular plates. We use the von Kármán nonlinear plate model to account for large deformations and study the effect of static deflections on the natural frequencies and mode shapes for six combinations of boundary conditions. The shooting method is used to solve the resulting eigenvalue problem. Our results show that static deformations have a significant effect on the natural frequencies and small effect on the mode shapes of the plate. Further, the results show that the presence of in-plane stresses has a significant effect on the natural frequencies.
A procedure for the calculation of flow through axisymmetric ducts
Directory of Open Access Journals (Sweden)
P. S. Heyns
1983-03-01
Full Text Available A procedure for the calculation of flow through axisymmetric ducts as are typically found in turbomachines, is presented. The procedure is based on a streamline curvature method with the governing equations formulated along quasi-orthogonals in the flow field. This formulation allows the procedure to be used for segments of a duct wherein the flow direction is predominantly radial. It is assumed that the flow on specific stream surfaces is isentropic, but normal entropy gradients may exist because of processes which took place upstream of the duct.
Axisymmetric fundamental solutions for a finite layer with impeded boundaries
Institute of Scientific and Technical Information of China (English)
程泽海; 陈云敏; 凌道盛; 唐晓武
2003-01-01
Axisymmetric fundamental solutions that are applied in the consolidation calculations of a finite clay layer with impeded boundaries were derived. Laplace and Hankel integral transforms were utilized with respect to time and radial coordinates, respectively in the analysis. The derivation of fundamental solutions considers two boundary-value problems involving unit point loading and ring loading in the vertical. The solutions are extended to circular distributed and strip distributed normal load. The computation and analysis of settlements, vertical total stress and excess pore pressure in the consolidation layer subject to circular loading are presented.
Stability and Halo Formation in Axisymmetric Intense Beams
Gluckstern, R L; Gluckstern, Robert L.; Kurennoy, Sergey S.
1998-01-01
Beam stability and halo formation in high-intensity axisymmetric 2D beams in a uniform focusing channel are analyzed using particle-in-cell simulations. The tune depression - mismatch space is explored for the uniform (KV) distribution of the particle transverse-phase-space density, as well as for more realistic ones (in particular, the water-bag distribution), to determine the stability limits and halo parameters. The numerical results show an agreement with predictions of the analytical model for halo formation (R.L. Gluckstern, Phys. Rev. Letters, 73 (1994) 1247).
Stability and Halo Formation in Axisymmetric Intense Beams.
Gluckstern, Robert L.; Kurennoy, Sergey S.
1997-05-01
Beam stability and halo formation in high-intensity axisymmetric 2D beams in a uniform focusing channel are analyzed using particle-in-cell simulations. The tune depression - mismatch space is explored for the uniform distribution of the particle transverse phase space density (Kapchinsky-Vladimirsky), as well as for more realistic ones (in particular, the water-bag distribution), to determine the stability limits and halo parameters. The numerical results obtained are compared and show an agreement with the predictions of the analytical model for halo formation developed earlier (R.L. Gluckstern, Phys. Rev. Lett., 73), 1247 (1994)..
Stability and halo formation in axisymmetric intense beams
Energy Technology Data Exchange (ETDEWEB)
Gluckstern, R.L. [Univ. of Maryland, College Park, MD (United States); Kurennoy, S.S. [Los Alamos National Lab., NM (United States)
1997-10-01
Beam stability and halo formation in high-intensity axisymmetric 2D beams in a uniform focusing channel are analyzed using particle-in-cell simulations. The tune depression-mismatch space is explored for the uniform (KV) distribution of the particle transverse-phase-space density, as well as for more realistic ones (in particular, the water-bag distribution), to determine the stability limits and halo parameters. The numerical results show an agreement with predictions of the analytical model for halo formation.
Modelling Acoustic Wave Propagation in Axisymmetric Varying-Radius Waveguides
DEFF Research Database (Denmark)
Bæk, David; Willatzen, Morten
2008-01-01
A computationally fast and accurate model (a set of coupled ordinary differential equations) for fluid sound-wave propagation in infinite axisymmetric waveguides of varying radius is proposed. The model accounts for fluid heat conduction and fluid irrotational viscosity. The model problem is solved...... by expanding solutions in terms of cross-sectional eigenfunctions following Stevenson’s method. A transfer matrix can be easily constructed from simple model responses of a given waveguide and later used in computing the response to any complex wave input. Energy losses due to heat conduction and viscous...
Area-angular-momentum inequality for axisymmetric black holes.
Dain, Sergio; Reiris, Martin
2011-07-29
We prove the local inequality A≥8π|J|, where A and J are the area and angular momentum of any axially symmetric closed stable minimal surface in an axially symmetric maximal initial data. From this theorem it is proved that the inequality is satisfied for any surface on complete asymptotically flat maximal axisymmetric data. In particular it holds for marginal or event horizons of black holes. Hence, we prove the validity of this inequality for all dynamical (not necessarily near equilibrium) axially symmetric black holes.
A simplified analytic form for generation of axisymmetric plasma boundaries
Luce, T. C.
2017-04-01
An improved method has been formulated for generating analytic boundary shapes as input for axisymmetric MHD equilibria. This method uses the family of superellipses as the basis function, as previously introduced. The improvements are a simplified notation, reduction of the number of simultaneous nonlinear equations to be solved, and the realization that not all combinations of input parameters admit a solution to the nonlinear constraint equations. The method tests for the existence of a self-consistent solution and, when no solution exists, it uses a deterministic method to find a nearby solution. Examples of generation of boundaries, including tests with an equilibrium solver, are given.
Exact solutions to some axisymmetric problems in magnetohydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Sheriazdanov, G.B.
1985-12-01
Steady-state axisymmetric flow of an incompressible perfectly conducting fluid is analyzed with allowance for the circular motion and the azimuthal component of the magnetic field. In the case of a nonviscous fluid, an equation of motion integral is obtained which relates the Bernoulli function to the azimuthal component of the velocity and magnetic fields. For the case of the rotation of a viscous fluid as a solid, the Bernoulli integral depends on the stream function, Reynolds and Alfven numbers, and the twisting parameter. 5 references.
Marginally stable circular orbits in stationary axisymmetric spacetimes
Beheshti, Shabnam
2015-01-01
We derive a necessary condition for the existence of marginally stable circular orbits of test particles in stationary axisymmetric spacetimes which possess a refection symmetry with respect to the equatorial plane; photon orbits are also addressed. Energy and angular momentum are shown to decouple from metric quantities, rendering a purely geometric characterization of circular orbits for this general class of metrics. The subsequent system is analyzed using resultants, providing an algorithmic approach for finding MSCO conditions. MSCOs are explicitly calculated for concrete examples of physical interest.
Quasi-static axisymmetric eversion hemispherical domes made of elastomers
Kabrits, Sergey A.; Kolpak, Eugeny P.
2016-06-01
The paper considers numerical solution for the problem of quasi-static axisymmetric eversion of a spherical shell (hemisphere) under action of external pressure. Results based on the general nonlinear theory of shells made of elastomers, proposed by K. F. Chernykh. It is used two models of shells based on the hypotheses of the Kirchhoff and Timoshenko, modified K.F. Chernykh for the case of hyperelastic rubber-like material. The article presents diagrams of equilibrium states of eversion hemispheres for both models as well as the shape of the shell at different points in the diagram.
Axisymmetric Vibration of Piezo-Lemv Composite Hollow Multilayer Cylinder
Directory of Open Access Journals (Sweden)
E. S. Nehru
2012-01-01
Full Text Available Axisymmetric vibration of an infinite piezolaminated multilayer hollow cylinder made of piezoelectric layers of 6 mm class and an isotropic LEMV (Linear Elastic Materials with Voids layers is studied. The frequency equations are obtained for the traction free outer surface with continuity conditions at the interfaces. Numerical results are carried out for the inner, middle, and outer hollow piezoelectric layers bonded by LEMV (It is hypothetical material layers and the dispersion curves are compared with that of a similar 3-layer model and of 3 and 5 layer models with inner, middle, and outer hollow piezoelectric layers bonded by CFRP (Carbon fiber reinforced plastics.
Using Elimination Theory to construct Rigid Matrices
Kumar, Abhinav; Patankar, Vijay M; N, Jayalal Sarma M
2009-01-01
The rigidity of a matrix A for target rank r is the minimum number of entries of A that must be changed to ensure that the rank of the altered matrix is at most r. Since its introduction by Valiant (1977), rigidity and similar rank-robustness functions of matrices have found numerous applications in circuit complexity, communication complexity, and learning complexity. Almost all nxn matrices over an infinite field have a rigidity of (n-r)^2. It is a long-standing open question to construct infinite families of explicit matrices even with superlinear rigidity when r=Omega(n). In this paper, we construct an infinite family of complex matrices with the largest possible, i.e., (n-r)^2, rigidity. The entries of an nxn matrix in this family are distinct primitive roots of unity of orders roughly exp(n^4 log n). To the best of our knowledge, this is the first family of concrete (but not entirely explicit) matrices having maximal rigidity and a succinct algebraic description. Our construction is based on elimination...
Directory of Open Access Journals (Sweden)
Karan Madan
2014-01-01
Full Text Available Background and Aim: Rigid bronchoscopy is often an indispensable procedure in the therapeutic management of a wide variety of tracheobronchial disorders. However, it is performed at only a few centers in adult patients in India. Herein, we report our initial 1-year experience with this procedure. Materials and Methods: A prospective observational study on the indications, outcomes, and safety of various rigid bronchoscopy procedures performed between November 2009 and October 2010. Improvement in dyspnea, cough, and the overall quality of life was recorded on a visual analog scale from 0 to 100 mm. A systematic review of PubMed was performed to identify studies reporting the use of rigid bronchoscopy from India. Results: Thirty-eight rigid bronchoscopies (50 procedures were performed in 19 patients during the study period. The commonest indication was benign tracheal stenosis followed by central airway tumor, and the procedures performed were rigid bronchoplasty, tumor debulking, and stent placement. The median procedure duration was 45 (range, 30-65 min. There was significant improvement in quality of life associated with therapeutic rigid bronchoscopy. Minor procedural complications were encountered in 18 bronchoscopies, and there was no procedural mortality. The systematic review identified 15 studies, all on the role of rigid bronchoscopy in foreign body removal. Conclusions: Rigid bronchoscopy is a safe and effective modality for treatment of a variety of tracheobronchial disorders. There is a dire need of rigid bronchoscopy training at teaching hospitals in India.
Omnidirectional Lamb waves by axisymmetrically-configured magnetostrictive patch transducer.
Lee, Joo Kyung; Kim, Hoe Woong; Kim, Yoon Young
2013-09-01
This work presents the generation of omnidirectional Lamb waves by a new magnetostrictive patch transducer (MPT) and investigates its generation mechanism. Although MPTs have been widely used for wave transduction in plates and pipes, no investigation reports the generation of omnidirectional Lamb waves in a plate by an MPT. For the generation, we propose an axisymmetrically-configured MPT that installs multiple axisymmetric turns of coil outside of a permanent cylindrical magnet located above the center of a circular magnetostrictive patch. After confirming the omnidirectivity of the proposed MPT experimentally, the mechanism of the Lamb wave generation and its frequency characteristics are investigated. It is also shown that the Lamb wave is most efficiently generated in a test plate when its wavelength is equal to two-thirds of the magnetostrictive patch diameter. If this wavelength¿patch diameter relation holds, the second radial extensional vibration mode of the patch of the proposed MPT is shown to be the mode responsible for generating the Lamb wave in a plate.
Non-axisymmetric instabilities in discs with imposed zonal flows
Vanon, R
2016-01-01
We conduct a linear stability calculation of an ideal Keplerian flow on which a sinusoidal zonal flow is imposed. The analysis uses the shearing sheet model and is carried out both in isothermal and adiabatic conditions, with and without self-gravity (SG). In the non-SG regime a structure in the potential vorticity (PV) leads to a non-axisymmetric Kelvin-Helmholtz (KH) instability; in the short-wavelength limit its growth rate agrees with the incompressible calculation by Lithwick (2007), which only considers perturbations elongated in the streamwise direction. The instability's strength is analysed as a function of the structure's properties, and zonal flows are found to be stable if their wavelength is $\\gtrsim 8H$, where $H$ is the disc's scale height, regardless of the value of the adiabatic index $\\gamma$. The non-axisymmetric KH instability can operate in Rayleigh-stable conditions, and it therefore represents the limiting factor to the structure's properties. Introducing SG triggers a second non-axisym...
Periodic body-and-bar frameworks
Borcea, Ciprian S; Tanigawa, Shin-ichi
2011-01-01
Abstractions of crystalline materials known as periodic body-and-bar frameworks are made of rigid bodies connected by fixed-length bars and subject to the action of a group of translations. In this paper, we give a Maxwell-Laman characterization for generic minimally rigid periodic body-and-bar frameworks. As a consequence we obtain efficient polynomial time algorithms for their recognition based on matroid partition and pebble games.
Tokamak magnetohydrodynamic equilibrium states with axisymmetric boundary and a 3D helical core.
Cooper, W A; Graves, J P; Pochelon, A; Sauter, O; Villard, L
2010-07-16
Magnetohydrodynamic (MHD) equilibrium states with imposed axisymmetric boundary are computed in which a spontaneous bifurcation develops to produce an internal three-dimensional (3D) configuration with a helical structure in addition to the standard axisymmetric system. Equilibrium states with similar MHD energy levels are shown to develop very different geometric structures. The helical equilibrium states resemble saturated internal kink mode structures.
A lower bound for the mass of axisymmetric connected black hole data sets
Chruściel, Piotr T
2011-01-01
We present a generalisation of the Brill-type proof of positivity of mass for axisymmetric initial data to initial data sets with black hole boundaries. The argument leads to a strictly positive lower bound for the mass of simply connected, connected axisymmetric black hole data sets in terms of the mass of a reference Schwarzschild metric.
Geodesic Acoustic Mode in Toroidally Axisymmetric Plasmas with Non-Circular Cross Sections
Institute of Scientific and Technical Information of China (English)
SHI Bing-Ren; LI Ji-Quan; DONG Jia-Qi
2005-01-01
@@ The geodesic acoustic mode in general toroidally axisymmetric plasmas such as Tokamak and spherical torus is studied in detail. The mode structure is found and the dispersion equation is derived and solved for arbitrary toroidally axi-symmetric plasmas. Besides the finite aspect ratio, effects of elongation and triangularity on this mode are clarified.
Topological Fluid Mechanics with Applications to Free Surfaces and Axisymmetric Flows
DEFF Research Database (Denmark)
Brøns, Morten
1996-01-01
Topological fluid mechanics is the study of qualitative features of fluid patterns. We discuss applications to the flow beneath a stagnant surface film, and to patterns in axisymmetric flow.......Topological fluid mechanics is the study of qualitative features of fluid patterns. We discuss applications to the flow beneath a stagnant surface film, and to patterns in axisymmetric flow....
1991-12-31
and stability for fluid flows, (with S.-J. Chern), Geop. and Astro. Fluid Dyn. 51, 1-4. %The energy-momentum method, (with Simo), La " Mecanique ... Analytique " de Lagrange et son H ritage, Atti della Accademia delle Scienze di Torino 124, 245-268. %Stability of coupled rigid bodies and geometrically