Xu, C; Wu, X; Wu, Xuejun
2004-01-01
In this paper, it is the first time to construct a complete post-Newtonian (PN) model of a rigid body by means of a new constraint on the mass current density and mass density. In our PN rigid body model most of relations, such as spin vector proportional to the angular velocity, the definition on the moment of inertia tensor, the key relation between the mass quadrupole moment and the moment of inertia tensor, rigid rotating formulae of mass quadrupole moment and the moment of inertia tensor, are just the extension of the main relations in Newtonian rigid body model. When all of $1/c^2$ terms are neglected, the PN rigid body model and the corresponding formulae reduce to Newtonian version. The key relation is obtained in this paper for the first time, which might be very useful in the future application to problems in geodynamics and astronomy.
Xu, Chongming; Tao, Jin-he; Wu, Xuejun
2003-01-01
In this paper, it is the first time to construct a complete post-Newtonian (PN) model of a rigid body by means of a new constraint on the mass current density and mass density. In our PN rigid body model most of relations, such as spin vector proportional to the angular velocity, the definition on the moment of inertia tensor, the key relation between the mass quadrupole moment and the moment of inertia tensor, rigid rotating formulae of mass quadrupole moment and the moment of inertia tensor...
Niebe, Sarah Maria
The topic of this thesis is the numerics of rigid body simulation, with focus on the contact force problem. Three contact force models are presented, followed by three contact point determination methods. To solve the contact force problem, six different numerical methods are presented, each...... tailored to solve problems in the form of one of the three contact force models. The scientific contributions of this thesis, lies in part in the dissection of existing methods in which issues are uncovered and – where possible – fixes are suggested, and in part in the development of novel methods. A...... contact point determination method, based on boolean surface maps, is developed to handle collisions between tetrahedral meshes. The novel nonsmooth nonlinear conjugate gradient (NNCG) method is presented. The NNCG method is comparable in terms of accuracy to the state-of-the-art method, projected Gauss...
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.
Real-Time Rigid Body Interactions
Fossum, Fredrik
2011-01-01
Rigid body simulations are useful in many areas, most notably video games and computer animation.However, the requirements for accuracy and performance vary greatly between applications.In this project we combine methods and techniques from different sources to implement a rigid body simulation.The simulation uses a particle representation to approximate objects with the intent of reaching better performance at the cost of accuracy.We simulate cubes in order to showcase the behavior of our si...
Quantum mechanics of a generalised rigid body
Gripaios, Ben; Sutherland, Dave
2016-05-01
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. We show how the method can be extended to cosets, generalising the linear rigid rotor. 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.
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.
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...
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
Brownian dynamics of confined rigid bodies
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.
Brownian dynamics of confined rigid bodies
Delong, Steven; Balboa Usabiaga, Florencio; Donev, Aleksandar
2015-10-01
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.
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...
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...
Propagation of Uncertainty in Rigid Body Attitude Flows
Lee, Taeyoung; Chaturvedi, Nalin A.; Sanyal, Amit K.; Leok, Melvin; McClamroch, N. Harris
2007-01-01
Motivated by attitude control and attitude estimation problems for a rigid body, computational methods are proposed to propagate uncertainties in the angular velocity and the attitude. The nonlinear attitude flow is determined by Euler-Poincar\\'e equations that describe the rotational dynamics of the rigid body acting under the influence of an attitude dependent potential and by a reconstruction equation that describes the kinematics expressed in terms of an orthogonal matrix representing the...
On the inertial motions of liquid-filled rigid bodies
Mazzone, Giusy; Galdi, Giovanni; Zunino, Paolo
2013-11-01
We consider a rigid body with a cavity completely filled by a viscous liquid and study the inertial motions of the system liquid-filled rigid body S . The equations governing the motion of this coupled system are given by the Navier-Stokes equations and the equations of the balance of the total angular momentum of S in absence of external forces and torques. Given any initial motion to the coupled system, characterized by an initial relative velocity of the fluid and an initial total angular momentum, we give a complete description of the behavior that the system liquid-filled rigid body will show at large times. From both analytical and numerical viewpoints, we are able to prove a longstanding conjecture stated by Zhukovskii, namely that S will eventually reach a steady state which is a rigid body permanent rotation. In other words, the liquid goes to rest with respect to the rigid body and the coupled system will rotate as a whole rigid body, with a constant angular velocity that is directed along one of the principal axes of inertia of the system.
Rigid multibody system dynamics with uncertain rigid bodies
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.
Kinematic Control of Free Rigid Bodies Using Dual Quaternions
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.
Global Controllability of Multidimensional Rigid Body by Few Torques
Sarychev, Andrey V
2009-01-01
We study global controllability of 'rotating' multidimensional rigid body (MRB) controlled by application of few torques. Study by methods of geometric control requires analysis of algebraic structure introduced by the quadratic term of Euler-Frahm equation. We discuss problems, which arise in the course of this analysis, and establish several global controllability criteria for damped and non damped cases.
Steady Fall of a Rigid Body in Viscous Fluid
Nečasová, Šárka
Praha : Ústav termomechaniky AV ČR, 2005 - (Příhoda, J.; Kozel, K.), s. 77-80 ISBN 80-85918-92-7. [Topical Problems of Fluid Mechanics. Prague (CZ), 25.02.2004] Institutional research plan: CEZ:AV0Z1019905 Keywords : steady fall * rigid body * viscous fluid Subject RIV: BA - General Mathematics
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
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.
Steady fall of a rigid body in viscous fluid
Nečasová, Šárka
2005-01-01
Roč. 63, Sp. Is. (2005), s. 2113-2119. ISSN 0362-546X. [Invited Talks from the Fourth World Congress of Nonlinear Analysts (WCNA 2004). Orlando, 30.7.2004-7.8.2004] R&D Projects: GA ČR(CZ) GA201/02/0684 Institutional research plan: CEZ:AV0Z1019905 Keywords : steady fall * rigid body * viscous fluid Subject RIV: BA - General Mathematics Impact factor: 0.519, year: 2005
Global Exponential Angular Velocity Observer for Rigid Body Systems
Berkane, Soulaimane; Abdessameud, Abdelkader; Tayebi, Abdelhamid
2016-01-01
We present a uniformly globally exponentially stable hybrid angular velocity observer for rigid body systems designed directly on $SO(3)\\times\\mathbb{R}^3$. The global exponential stability result makes this observer a good candidate for a controller-observer combination with a guaranteed separation property. Simulation results are provided to demonstrate the effectiveness of the proposed hybrid observer as a part of an attitude stabilization scheme.
Stability of relative equilibria of multidimensional rigid body
Izosimov, Anton
2012-01-01
It is well known that a free three-dimensional rigid body admits three stationary rotations. These are the rotations around three principal axes of inertia. The rotations around the long and the short axes are stable, while the rotation around the intermediate axis is unstable. We generalize this result to the case of a multidimensional body. The stability problem is being solved for a dense subset of stationary rotations in arbitrary dimension.
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
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.
Failure of intuition in elementary rigid body dynamics
Lemos, Nivaldo A
2008-01-01
Suppose a projectile collides perpendicularly with a stationary rigid rod on a smooth horizontal table. We show that, contrary to what one naturally expects, it is not always the case that the rod acquires maximum angular velocity when struck at an extremity. The treatment is intended for first year university students of Physics or Engineering, and could form the basis of a tutorial discussion of conservation laws in rigid body dynamics.
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 ...
Geometry of the Motion of Ideal Fluids and Rigid Bodies
Rajeev, S G
2009-01-01
Arnold pointed out that the Euler equation of incompressible ideal hydrodynamics describes geodesics on the group of volume-preserving diffeomorphisms. A simple analogue is the Euler equation for a rigid body, which is the geodesic equation on the rotation group with respect to a metric determined by the moment of inertia. The metric on the group is left-invariant but not right-invariant. We will reduce the geometry of such groups (using techniques popularized by Milnor) to algebra on their tangent space. In particular, the curvature can be expressed as a biquadratic form on the Lie algebra. Arnold's result that motion of incompressible fluids has instabilities (due to the sectional curvature being negative) can be recovered more simply. Surprisingly, such an instability arises in rigid body mechanics as well: the metric on SO(3) corresponding to the moment of inertia of a thin cylinder (coin) has negative sectional curvature in one tangent plane. Both ideal fluids and rigid bodies can be thought of as hamilt...
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
Dynamic Buckling of Column Impacted by a Rigid Body
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.
Euler-Poincare Reduction of a Rigid Body Motion
Wisniewski, Rafal; Kulczycki, P.
2005-01-01
|If a mechanical system experiences symmetry, the Lagrangian becomes invariant under a certain group action. This property leads to substantial simplification of the description of movement. The standpoint in this article is a mechanical system afected by an external force of a control action...... control system generates an external force, which may break the symmetry in the dynamics. This paper shows how to model and to control a mechanical sys- tem on the reduced phase space, such that complete state space asymptotic stabilization can be achieved. The paper comprises a specialization of the well......-known Euler-Poincare reduction to a rigid body motion with forcing....
Euler-Poincare Reduction of Externall Forced Rigid Body Motion
Wisniewski, Rafal; Kulczycki, P.
2004-01-01
If a mechanical system experiences symmetry, the Lagrangian becomes invariant under a certain group action. This property leads to substantial simplification of the description of movement. The standpoint in this article is a mechanical system affected by an external force of a control action...... control system generates an external force, which may break the symmetry in the dynamics. This paper shows how to model and to control a mechanical system on the reduced phase space, such that complete state space asymptotic stabilization can be achieved. The paper comprises a specialization of the well......-known Euler-Poincaré reduction to a rigid body motion with forcing....
Identification of Helicopter Rigid Body Dynamics from Flight Data.
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.
Collisions of Constrained Rigid Body Systems with Friction
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.
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.
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.
A general purpose nonlinear rigid body mass finite element for application to rotary wing dynamics
Hamilton, B. K.; Straub, F. K.; Ruzicka, G. C.
1991-01-01
The Second Generation Comprehensive Helicopter Analysis System employs the present formulation of the general-purpose nonlinear rigid body mass finite element, which represents the hub masses, blade tip masses, and pendulum vibration absorbers. The rigid body mass element has six degrees of freedom, and accounts for gravitational as well as dynamic effects. A consequence of deriving the element's equations from various physical principles is that, prior to the transformation which couples the rigid body mass element to the rotor blade finite element, the forces obtained for each element are fundamentally different; this is true notwithstanding the degrees-of-freedom of each element are parameterized using the same coordinates.
Error analysis of rigid body posture measurement system based on circular feature points
Huo, Ju; Cui, Jishan; Yang, Ning
2015-02-01
For monocular vision pose parameters determine the problem, feature-based target feature points on the plane quadrilateral, an improved two-stage iterative algorithm is proposed to improve the optimization of rigid body posture measurement calculating model. Monocular vision rigid body posture measurement system is designed; experimentally in each coordinate system determined coordinate a unified method to unify the each feature point measure coordinates; theoretical analysis sources of error from rigid body posture measurement system simulation experiments. Combined with the actual experimental analysis system under the condition of simulation error of pose accuracy of measurement, gives the comprehensive error of measurement system, for improving measurement precision of certain theoretical guiding significance.
Kinematic simulation of human gait with a multi-rigid-body foot model
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.
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.
Non-existence of Physical Classical Solutions to Euler's Equations of Rigid Body Dynamics
Wilkinson, Mark
2015-01-01
We prove that one cannot construct, for arbitrary initial data, global-in-time physical classical solutions to Euler's equations of continuum rigid body mechanics when the constituent rigid bodies are not perfect spheres. By 'physical' solutions, we mean those that conserve the total linear momentum, angular momentum and kinetic energy of any given initial datum. The reason for absence of classical solutions is due to the non-existence of velocity scattering maps which resolve a collision bet...
Rigid Body Inertia Estimation Using Extended Kalman and Savitzky-Golay Filters
Donghoon Kim; Sungwook Yang; Sangchul Lee
2016-01-01
Inertia properties of rigid body such as ground, aerial, and space vehicles may be changed by several occasions, and this variation of the properties influences the control accuracy of the rigid body. For this reason, accurate inertia properties need to be obtained for precise control. An estimation process is required for both noisy gyro measurements and the time derivative of the gyro measurements. In this paper, an estimation method is proposed for having reliable estimates of inertia prop...
Bounded attitude control of rigid bodies: Real-time experimentation to a quadrotor mini-helicopter
Guerrero-Castellanos, Fermi; Marchand, Nicolas; Hably, Ahmad; Lesecq, Suzanne; Delamare, Jérôme
2011-01-01
A quaternion-based feedback is developed for the attitude stabilization of rigid bodies. The control design takes into account a priori input bounds and is based on nested saturation approach. It results in a very simple controller suitable for an embedded use with low computational resources available. The proposed method is generic not restricted to symmetric rigid bodies and does not require the knowledge of the inertia matrix of the body. The control law can be tuned to force closed-loop ...
Contact Point Generation for Convex Polytopes in Interactive Rigid Body Dynamics
Silcowitz-Hansen, Morten; Niebe, Sarah Maria; 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...
Geometric relations between rigid bodies (Part 2): From semantics to software
De Laet T.; Bellens S.; Bruyninckx H.; De Schutter J.
2013-01-01
Rigid bodies are essential primitives in the modelling of robotic devices, tasks, and percep- tion. Basic geometric relations between rigid bodies in- clude relative position, orientation, pose, linear veloc- ity, angular velocity, twist, force, torque, and wrench. In Part 1, we explicitly stated the semantics of all coordinate-invariant properties and operations, and, more importantly, all the choices that are made in co- ordinate representations of these geometric re...
Elastic Plates in Multibody Systems: A Treatment Using Existing Rigid Body Codes
In the present paper, it is shown how one can employ existing rigid body codes to handle systems containing elastic plates by using a Rayleigh-Ritz discretization procedure. The equations of motion are formulated for a rectangular plate undergoing large rigid body motions but small elastic deformations. Geometric nonlinearities in the elastic coordinates are taken into account to include the effect of dynamic stiffening. As an example, a spin-up maneuver for a simply-supported plate is treated
Estimating the orientation of a rigid body moving in space using inertial sensors
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.
Estimating the orientation of a rigid body moving in space using inertial sensors
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
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.
New optimal control laws for attitude of a rigid body motion without angular velocity measurements
El-Gohary, Awad [Department of Statistics and Operational Research, Faculty of Science King Saud University, P.O. Box 2455, Riyadh 11451 (Saudi Arabia)] e-mail: aigohary@ksu.edu.sa
2005-08-01
In this paper we shall use the passive properties of Euler dynamic equations as well as the structural properties of kinematic equations in terms of Cayley-Rodrigues and Modified Rodrigues parameters to derive optimal control laws without any information about the angular velocity of the rigid body. The interesting difference in the current study is the assumption that only the kinematics attitude parameters are available for the control process. The optimal control laws ensure the optimal asymptotic stability of the rigid body motion and minimize a selecting performance are obtained in terms of the kinematics attitude parameters and their estimates. Numerical examples are presented to demonstrate the theoretical results.
Physical pendulum—a simple experiment can give comprehensive information about a rigid body
Kladivová, Mária; Mucha, L'ubomír
2014-03-01
A simple experiment with a physical pendulum examining some aspects of rigid body motion is presented in this paper. The experiment consists of measuring the period of oscillation of a rod with non-homogeneous mass distribution used as a physical pendulum, dependent upon the position of the pivot axis. The obtained dependence provides sufficient information to calculate the position of the centre of mass, moment of inertia of the rigid body and local gravitational acceleration. This experiment is intended for secondary school and undergraduate students.
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
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 proposes discontinuous feedback laws to achieve asymptotic stability with exponential convergence rates
Patrinopoulos, Matthaios; Kefalis, Chrysovalantis
2015-12-01
In this paper, we focus on smartphones as experimental tools; specifically we use the gyroscope sensor of a smartphone to study the turning motion of a rigid body. Taking into consideration recent work concerning that topic, we try to use the gyroscope sensor in studying the complex motion of a rolling cylinder on a slope.
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…
Reverse rotations in the circularly-driven motion of a rigid body
Parisio, Fernando
2008-01-01
We study the dynamical response of a circularly-driven rigid body, focusing on the description of intrinsic rotational behavior (reverse rotations). The model system we address is integrable but nontrivial, allowing for qualitative and quantitative analysis. A scale free expression defining the separation between possible spinning regimes is obtained.
On the linear problem arising from motion of a fluid around a moving rigid body
Nečasová, Šárka; Wolf, J.
2015-01-01
Roč. 140, č. 2 (2015), s. 241-259. ISSN 0862-7959 R&D Projects: GA ČR(CZ) GAP201/11/1304 Institutional support: RVO:67985840 Keywords : incompressible fluid * rotating rigid body * strong solution Subject RIV: BA - General Mathematics http://hdl.handle.net/10338.dmlcz/144329
Silcowitz, Morten; Niebe, Sarah Maria; Erleben, Kenny
2009-01-01
n interactive physical simulation, contact forces are applied to prevent rigid bodies from penetrating each other. Accurate contact force determination is a computationally hard problem. Thus, in practice one trades accuracy for performance. The result is visual artifacts such as viscous or damped...
Projected Gauss-Seidel Subspace Minimization Method for Interactive Rigid Body Dynamics
Silcowitz, Morten; Niebe, Sarah Maria; 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...
Reconstructing rotations and rigid body motions from exact point correspondences through reflections
D. Fontijne; L. Dorst
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
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...
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.
Controlling Mixing Inside a Droplet by Time Dependent Rigid-body Rotation
Chabreyrie, R; Chandre, C; Singh, P; Aubry, N
2008-01-01
The use of microscopic discrete fluid volumes (i.e., droplets) as microreactors for digital microfluidic applications often requires mixing enhancement and control within droplets. In this work, we consider a translating spherical liquid droplet to which we impose a time periodic rigid-body rotation which we model using the superposition of a Hill vortex and an unsteady rigid body rotation. This perturbation in the form of a rotation not only creates a three-dimensional chaotic mixing region, which operates through the stretching and folding of material lines, but also offers the possibility of controlling both the size and the location of the mixing. Such a control is achieved by judiciously adjusting the three parameters that characterize the rotation, i.e., the rotation amplitude, frequency and orientation of the rotation. As the size of the mixing region is increased, complete mixing within the drop is obtained.
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.
Compliant mechanism road bicycle brake: a rigid-body replacement case study
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.
Conservative rigid body dynamics by convected base vectors with implicit constraints
Krenk, Steen; Nielsen, Martin Bjerre
2014-01-01
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......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......-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...
On the long-time behaviour of a rigid body immersed in a viscous fluid
Feireisl, Eduard; Nečasová, Šárka
2011-01-01
Roč. 90, č. 1 (2011), s. 59-66. ISSN 0003-6811 R&D Projects: GA ČR GA201/09/0917; GA AV ČR IAA100190804 Institutional research plan: CEZ:AV0Z10190503 Keywords : rigid body * viscous fluid * Navier-Stokes system Subject RIV: BA - General Mathematics Impact factor: 0.744, year: 2011 http://www.tandfonline.com/doi/abs/10.1080/00036811003735964
Inertial Vector Based Attitude Stabilization of Rigid Body Without Angular Velocity Measurements
Benziane, L.; Benallegue, A.; Chitour, Y.; Tayebi, A.
2015-01-01
We address the problem of attitude stabilization of a rigid body, in which neither the angular velocity nor the instantaneous measurements of the attitude are used in the feedback, only body vector measurements are needed. The design of the controller is based on an angular velocity observer-like system, where a first order linear auxiliary system based directly on vector measurements is introduced. The introduction of gain matrices provides more tuning flexibility and better results compared...
Fitzpatrick, P. M.; Harmon, G. R.; Cochran, J. E.; Shaw, W. A.
1974-01-01
Some methods of approaching a solution to the Hamilton-Jacobi equation are outlined and examples are given to illustrate particular methods. These methods may be used for cases where the Hamilton-Jacobi equation is not separable and have been particularly useful in solving the rigid body motion of an earth satellite subjected to gravity torques. These general applications may also have usefulness in studying the motion of satellites with aerodynamic torque and in studying space vehicle motion where thrusting is involved.
Geometric Tracking Control of the Attitude Dynamics of a Rigid Body on SO(3)
Lee, Taeyoung
2010-01-01
This paper provides new results for a tracking control of the attitude dynamics of a rigid body. Both of the attitude dynamics and the proposed control system are globally expressed on the special orthogonal group, to avoid complexities and ambiguities associated with other attitude representations such as Euler angles or quaternions. By selecting an attitude error function carefully, we show that the proposed control system guarantees a desirable tracking performance uniformly for nontrivial...
Stability Analysis of a Rigid Body with a Flexible Attachment Using the Energy-Casimir Method
Posbergh, T. A.; Krishnaprasad, Perinkulam S.; Marsden, Jerrold E.
1987-01-01
We consider a system consisting of a rigid body to which a linear extensible shear beam is attached. For such a system the Energy-Casimir method can be used to investigate the stability of the equilibria. In the case we consider, it can be shown that a test for (formal) stability reduces to checking the positive definiteness of two matrices which depend on the parameters of the system and the particular equilibrium about which the stability is to be ascertained.
The phase topology of a special case of Goryachev integrability in rigid body dynamics
Ryabov, P. E., E-mail: orelryabov@mail.ru [Financial University under the Government of the Russian Federation, Moscow (Russian Federation)
2014-07-31
The phase topology of a special case of Goryachev integrability in the problem of motion of a rigid body in a fluid is investigated using the method of Boolean functions, which was developed by Kharlamov for algebraically separated systems. The bifurcation diagram of the moment map is found and the Fomenko invariant, which classifies the systems up to rough Liouville equivalence, is specified. Bibliography: 15 titles. (paper)
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.
A stable FSI algorithm for light rigid bodies in compressible flow
Banks, J. W.; Henshaw, W. D.; Sjögreen, B.
2013-07-01
In this article we describe a stable partitioned algorithm that overcomes the added mass instability arising in fluid-structure interactions of light rigid bodies and inviscid compressible flow. The new algorithm is stable even for bodies with zero mass and zero moments of inertia. The approach is based on a local characteristic projection of the force on the rigid body and is a natural extension of the recently developed algorithm for coupling compressible flow and deformable bodies [1-3]. The new algorithm advances the solution in the fluid domain with a standard upwind scheme and explicit time-stepping. The Newton-Euler system of ordinary differential equations governing the motion of the rigid body is augmented by added mass correction terms. This system, which is very stiff for light bodies, is solved with an A-stable diagonally implicit Runge-Kutta scheme. The implicit system (there is one independent system for each body) consists of only 3d+d2 scalar unknowns in d=2 or d=3 space dimensions and is fast to solve. The overall cost of the scheme is thus dominated by the cost of the explicit fluid solver. Normal mode analysis is used to prove the stability of the approximation for a one-dimensional model problem and numerical computations confirm these results. In multiple space dimensions the approach naturally reveals the form of the added mass tensors in the equations governing the motion of the rigid body. These tensors, which depend on certain surface integrals of the fluid impedance, couple the translational and angular velocities of the body. Numerical results in two space dimensions, based on the use of moving overlapping grids and adaptive mesh refinement, demonstrate the behavior and efficacy of the new scheme. These results include the simulation of the difficult problems of shock impingement on an ellipse and a more complex body with appendages, both with zero mass.
Rigid Body Time Integration by Convected Base Vectors with Implicit Constraints
Krenk, Steen; Nielsen, Martin Bjerre
2013-01-01
A conservative time integration algorithm based on a convected set of orthonormal base vectors is presented. The equations of motion are derived from an extended Hamiltonian formulation, combining the components of the three base vectors with a set of orthonormality constraints. The particular form 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 strai...
Efficient time-symmetric simulation of torqued rigid bodies using Jacobi elliptic functions
Celledoni, E.; Säfström, N.
2006-05-01
If the three moments of inertia are distinct, the solution to the Euler equations for the free rigid body is given in terms of Jacobi elliptic functions. Using the arithmetic-geometric mean algorithm (Abramowitz and Stegun 1992 Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (New York: Dover)), these functions can be calculated efficiently and accurately. Compared to standard numerical ODE and Lie-Poisson solvers, the overall approach yields a faster and more accurate numerical solution to the Euler equations. This approach is designed for mass asymmetric rigid bodies. In the case of symmetric bodies, the exact solution is available in terms of trigonometric functions, see Dullweber et al (1997 J. Chem. Phys. 107 5840-51), Reich (1996 Fields Inst. Commun. 10 181-91) and Benettin et al (2001 SIAM J. Sci. Comp. 23 1189-203) for details. In this paper, we consider the case of asymmetric rigid bodies subject to external forces. We consider a strategy similar to the symplectic splitting method proposed in Reich (1996 Fields Inst. Commun. 10 181-91) and Dullweber et al (1997 J. Chem. Phys. 107 5840-51). The method proposed here is time-symmetric. We decompose the vector field of our problem into a free rigid body (FRB) problem and another completely integrable vector field. The FRB problem consists of the Euler equations and a differential equation for the 3 × 3 orientation matrix. The Euler equations are integrated exactly while the matrix equation is approximated using a truncated Magnus series. In our experiments, we observe that the overall numerical solution benefits greatly from the very accurate solution of the Euler equations. We apply the method to the heavy top and the simulation of artificial satellite attitude dynamics.
Efficient time-symmetric simulation of torqued rigid bodies using Jacobi elliptic functions
If the three moments of inertia are distinct, the solution to the Euler equations for the free rigid body is given in terms of Jacobi elliptic functions. Using the arithmetic-geometric mean algorithm (Abramowitz and Stegun 1992 Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (New York: Dover)), these functions can be calculated efficiently and accurately. Compared to standard numerical ODE and Lie-Poisson solvers, the overall approach yields a faster and more accurate numerical solution to the Euler equations. This approach is designed for mass asymmetric rigid bodies. In the case of symmetric bodies, the exact solution is available in terms of trigonometric functions, see Dullweber et al (1997 J. Chem. Phys. 107 5840-51), Reich (1996 Fields Inst. Commun. 10 181-91) and Benettin et al (2001 SIAM J. Sci. Comp. 23 1189-203) for details. In this paper, we consider the case of asymmetric rigid bodies subject to external forces. We consider a strategy similar to the symplectic splitting method proposed in Reich (1996 Fields Inst. Commun. 10 181-91) and Dullweber et al (1997 J. Chem. Phys. 107 5840-51). The method proposed here is time-symmetric. We decompose the vector field of our problem into a free rigid body (FRB) problem and another completely integrable vector field. The FRB problem consists of the Euler equations and a differential equation for the 3 x 3 orientation matrix. The Euler equations are integrated exactly while the matrix equation is approximated using a truncated Magnus series. In our experiments, we observe that the overall numerical solution benefits greatly from the very accurate solution of the Euler equations. We apply the method to the heavy top and the simulation of artificial satellite attitude dynamics
In silico single-molecule manipulation of DNA with rigid body dynamics.
Pascal Carrivain; Maria Barbi; Jean-Marc Victor
2014-01-01
We develop a new powerful method to reproduce in silico single-molecule manipulation experiments. We demonstrate that flexible polymers such as DNA can be simulated using rigid body dynamics thanks to an original implementation of Langevin dynamics in an open source library called Open Dynamics Engine. We moreover implement a global thermostat which accelerates the simulation sampling by two orders of magnitude. We reproduce force-extension as well as rotation-extension curves of reference ex...
Molina, John Jairo; Yamamoto, Ryoichi
2013-01-01
An improved formulation of the Smoothed Profile method is introduced to perform direct numerical simulations of arbitrary rigid body dispersions in a Newtonian host solvent. Previous implementations of the method were restricted to spherical particles, severely limiting the types of systems that could be studied. The validity of the method is carefully examined by computing the friction/mobility tensors for a wide variety of geometries and comparing them to reference values obtained from accu...
Molina, John J; Yamamoto, Ryoichi
2013-12-21
An improved formulation of the "Smoothed Profile" method is introduced to perform direct numerical simulations of arbitrary rigid body dispersions in a Newtonian host solvent. Previous implementations of the method were restricted to spherical particles, severely limiting the types of systems that could be studied. The validity of the method is carefully examined by computing the friction/mobility tensors for a wide variety of geometries and comparing them to reference values obtained from accurate solutions to the Stokes-Equation. PMID:24359350
Modeling the bacterial flagellum by an elastic network of rigid bodies
Speier, C.; Vogel, R.; Stark, H.
2011-08-01
Bacteria such as Escherichia coli propel themselves by rotating a bundle of helical filaments, each driven by a rotary motor embedded in the cell membrane. Each filament is an assembly of thousands of copies of the protein flagellin which assumes two different states. We model the filament by an elastic network of rigid bodies that form bonds with one another according to a scheme suggested by Namba and Vondervistz (1997 Q. Rev. Biophys. 30 1-65) and add additional binding sites at the inner part of the rigid body. Our model reproduces the helical parameters of the 12 possible polymorphic configurations very well. We demonstrate that its energetical ground state corresponds to the normal helical form, usually observed in nature, only when inner and outer binding sites of the rigid body have a large axial displacement. This finding correlates directly to the elongated shape of the flagellin molecule. An Ising Hamiltonian in our model directly addresses the two states of the flagellin protein. It contains an external field that represents external parameters which allow us to alter the ground state of the filament.
Wang, Chengjie; Eldredge, Jeff D.
2015-08-01
A strong coupling algorithm is presented for simulating the dynamic interactions between incompressible viscous flows and rigid-body systems in both two- and three-dimensional problems. In this work, the Navier-Stokes equations for incompressible flow are solved on a uniform Cartesian grid by the vorticity-based immersed boundary projection method of Colonius and Taira. Dynamical equations for arbitrary rigid-body systems are also developed. The proposed coupling method attempts to unify the treatment of constraints in the fluid and structure-the incompressibility of the fluid, the linkages in the rigid-body system, and the conditions at the interface-through the use of Lagrange multipliers. The resulting partitioned system of equations is solved with a simple relaxation scheme, based on an identification of virtual inertia from the fluid. The scheme achieves convergence in only 2 to 5 iterations per time step for a wide variety of mass ratios. The formulation requires that only a subset of the discrete fluid equations be solved in each iteration. Several two- and three-dimensional numerical tests are conducted to validate and demonstrate the method, including a falling cylinder, flapping of flexible wings, self-excited oscillations of a system of many linked plates in a free stream, and passive pivoting of a finite aspect ratio plate under the influence of gravity in a free stream. The results from the current method are compared with previous experimental and numerical results and good agreement is achieved.
Rigid Body Modes Influence On Microvibration Analysis-Application To Swarm
Laduree, G.; Fransen, S.; Baldesi, G.; Pflieger, I.
2012-07-01
Microvibrations are defined as low level mechanical disturbances affecting payload performance, generated by mobile parts or mechanism operating on-board the spacecraft, like momentum or reaction wheels, pointing mechanism, cryo-coolers or thrusters. The disturbances caused by these sources are transmitted through the spacecraft structure and excite modes of that structure or elements of the payload impacting its performance (e.g. Line of sight rotations inducing some image quality degradation). The dynamic interaction between these three elements (noise source, spacecraft structure and sensitive receiver) makes the microvibration prediction a delicate problem. Microvibration sources are generally of concern in the frequency range from a few Hz to 1000 Hz. However, in some specific cases, high stability at lower frequencies might be requested. This is the case of the SWARM mission, whose objectives are to provide the best ever survey of the geomagnetic field and its temporal evolution as well as supplementary information for studying the interaction of the magnetic field with other physical quantities describing the Earth system (e.g. ocean circulation). Among its instruments, SWARM is embarking a very sensitive 6-axis accelerometer in the low frequency range (10-8 m/s2 or rad/s2 between 10-4 and 0.1 Hz) located at its Centre of Gravity and an Absolute Scalar Magnetometer located at the tip of a boom far from the spacecraft body. The ASM performs its measurements by rotating an alternative magnetic field around its main axis thanks to a piezo-electric motor. This repeated disturbance might generate some pollution of the accelerometer science data. The objective of this work is to focus on the interaction of the rigid body mode calculation method with the elastic contribution of the normal modes excited by the noise source frequency content. It has indeed been reported in the past that NASTRAN Lanczos rigid body modes may lead to inaccurate rigid-body accelerations
The tennis racket effect in a three-dimensional rigid body
L van Damme; Mardesic, P.; 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. ...
On Classical Dynamics of Affinely-Rigid Bodies Subject to the Kirchhoff-Love Constraints
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.
Euler-Poincaré Reduction of Externally Forced Rigid Body Motion
Wisniewski, Rafal; Kulczycki, P.
2004-01-01
If a mechanical system experiences symmetry, the Lagrangian becomes invariant under a certain group action. This property leads to substantial simplification of the description of movement. The standpoint in this article is a mechanical system affected by an external force of a control action...... control system generates an external force, which may break the symmetry in the dynamics. This paper shows how to model and to control a mechanical system on the reduced phase space, such that complete state space asymptotic stabilization can be achieved. The paper comprises a specialization of the well......-known Euler-Poincaré reduction to a rigid body motion with forcing....
Inertial Motions of a Rigid Body with a cavity filled with a viscous liquid
Galdi, Giovanni P.; Mazzone, Giusy; Zunino, Paolo
2014-01-01
We study inertial motions of the coupled system, S, constituted by a rigid body containing a cavity that is completely filled with a viscous liquid. We show that for data of arbitrary size (initial kinetic energy and total angular momentum) every weak solution (a la Leray-Hopf) converges, as time goes to infinity, to a uniform rotation, thus proving a famous "conjecture" of Zhukovskii. Moreover we show that, in a wide range of initial data, this rotation must occur along the central axis of i...
Rigid Body Time Integration by Convected Base Vectors with Implicit Constraints
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......A conservative time integration algorithm based on a convected set of orthonormal base vectors is presented. The equations of motion are derived from an extended Hamiltonian formulation, combining the components of the three base vectors with a set of orthonormality constraints. The particular form...
Asymptotic behaviour of a rigid body with a cavity filled by a viscous liquid
Disser, Karoline
2014-01-01
We consider the system of equations modeling the free motion of a rigid body with a cavity filled by a viscous (Navier-Stokes) liquid. We give a rigorous proof of Zhukovskiy's Theorem, which states that in the limit of time going to infinity, the relative fluid velocity tends to zero and the rigid velocity of the full structure tends to a steady rotation around one of the principle axes of inertia. The existence of global weak solutions for this system was established previously. In particula...
On the identifiability of a rigid body moving in a stationary viscous fluid
This paper is devoted to a geometrical inverse problem associated with a fluid–structure system. More precisely, we consider the interaction between a moving rigid body and a viscous and incompressible fluid. Assuming a low Reynolds regime, the inertial forces can be neglected and, therefore, the fluid motion is modelled by the Stokes system. We first prove the well posedness of the corresponding system. Then we show an identifiability result: with one measure of the Cauchy forces of the fluid on one given part of the boundary and at some positive time, the shape of a convex body and its initial position are identified. (paper)
Comparison of Point and Line Features and Their Combination for Rigid Body Motion Estimation
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...... means of SIFT descriptors). All features are then matched across stereo and time, and we use these correspondences to estimate the RBM by solving the 3D-2D pose estimation problem. We test dierent feature sets on various stereo image sequences, recorded in realistic outdoor and indoor scenes. We...
Conservative integration of rigid body motion by quaternion parameters with implicit constraints
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 symmetric...... equations via the set of momentum equations. Initially, the normalization of the quaternion array is introduced via a Lagrange multiplier. However, this Lagrange multiplier can be expressed explicitly in terms of the gradient of the external load potential, and elimination of the Lagrange multiplier from...
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
Modeling and experimentation with asymmetric rigid bodies: a variation on disks and inclines
We study the ascending motion of a disk rolling on an incline when its centre of mass lies outside the disk axis. The problem is suitable as laboratory project for a first course in mechanics at the undergraduate level and goes beyond typical textbook problems about bi-dimensional rigid body motions. We develop a theoretical model for the disk motion based on mechanical energy conservation and compare its predictions with experimental data obtained by digital video recording. Using readily available resources, a very satisfactory agreement is obtained between the model and the experimental observations. These results complement previous ones that have been reported in the literature for similar systems. (paper)
Modeling of multibody dynamics with flexible links is a challenging task, which not only involves the effect of rigid body motion on elastic deformations, but also includes the influence of elastic deformations on rigid body motion. This paper presents coupling characteristics of rigid body motions and elastic motions of a 3-PRR parallel manipulator with three flexible intermediate links. The intermediate links are modeled as Euler-Bernoulli beams with pinned-pinned boundary conditions based on the assumed mode method (AMM). Using Lagrange multipliers, the fully coupled equations of motions of the flexible parallel manipulator are developed by incorporating the rigid body motions with elastic motions. The mutual dependence of elastic deformations and rigid body motions are investigated from the analysis of the derived equations of motion. Open-loop simulation without joint motion controls and closed-loop simulation with joint motion controls are performed to illustrate the effect of elastic motion on rigid body motions and the coupling effect amongst flexible links. These analyses and results provide valuable insight to the design and control of the parallel manipulator with flexible intermediate links
Zhang Xuping, E-mail: zhxp@mie.utoronto.ca; Mills, James K., E-mail: mills@mie.utoronto.ca; Cleghorn, William L. [University of Toronto, Department of Mechanical and Industrial Engineering (Canada)], E-mail: cleghrn@mie.utoronto.ca
2009-03-15
Modeling of multibody dynamics with flexible links is a challenging task, which not only involves the effect of rigid body motion on elastic deformations, but also includes the influence of elastic deformations on rigid body motion. This paper presents coupling characteristics of rigid body motions and elastic motions of a 3-PRR parallel manipulator with three flexible intermediate links. The intermediate links are modeled as Euler-Bernoulli beams with pinned-pinned boundary conditions based on the assumed mode method (AMM). Using Lagrange multipliers, the fully coupled equations of motions of the flexible parallel manipulator are developed by incorporating the rigid body motions with elastic motions. The mutual dependence of elastic deformations and rigid body motions are investigated from the analysis of the derived equations of motion. Open-loop simulation without joint motion controls and closed-loop simulation with joint motion controls are performed to illustrate the effect of elastic motion on rigid body motions and the coupling effect amongst flexible links. These analyses and results provide valuable insight to the design and control of the parallel manipulator with flexible intermediate links.
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.
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.
Rigid Body Inertia Estimation Using Extended Kalman and Savitzky-Golay Filters
Donghoon Kim
2016-01-01
Full Text Available Inertia properties of rigid body such as ground, aerial, and space vehicles may be changed by several occasions, and this variation of the properties influences the control accuracy of the rigid body. For this reason, accurate inertia properties need to be obtained for precise control. An estimation process is required for both noisy gyro measurements and the time derivative of the gyro measurements. In this paper, an estimation method is proposed for having reliable estimates of inertia properties. First, the Euler equations of motion are reformulated to obtain a regressor matrix. Next, the extended Kalman filter is adopted to reduce the noise effects in gyro angular velocity measurements. Last, the inertia properties are estimated using linear least squares. To achieve reliable and accurate angular accelerations, a Savitzky-Golay filter based on an even number sampled data is utilized. Numerical examples are presented to demonstrate the performance of the proposed algorithm for the case of a space vehicle. The numerical simulation results show that the proposed algorithm provides accurate inertia property estimates in the presence of noisy measurements.
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.
Gerstmayr, J.; Holl, H.J.; Irschik, H. [Inst. of Mechanics and Machine Design, Johannes Kepler University of Linz (Austria)
2001-03-01
A numerical algorithm for studying the development of plastic and damaged zones in a vibrating structural element with a large, guided rigid-body motion is presented. Beam-type elements vibrating in the small-strain regime are considered. A machine element performing rotatory motions, similar to an element of a slider-crank mechanism, is treated as a benchmark problem. Microstructural changes in the deforming material are described by the mesolevel variables of plastic strain and damage, which are consistently included into a macroscopic analysis of the overall beam motion. The method is based on an eigenstrain formulation, considering plastic strain and damage to contribute to an eigenstrain loading of a linear elastic background structure. Rigid-body coordinates are incorporated into this beam-type structural formulation, and an implicit numerical scheme is presented for iterative computation of the eigenstrains from the mesolevel constitutive behavior. Owing to the eigenstrain formulation, any of the existing constitutive models with internal variables could in principle be implemented. Linear elastic/perfectly plastic behavior is exemplarily treated in a numerical study, where plastic strain is connected to the Kachanov damage parameter by a simple damage law. Inelastic effects like plastic shakedown and damage-induced low-cycle rupture are shown to occur in the examplary problems. (orig.)
The Serret-Andoyer Formalism in Rigid-Body Dynamics: I. Symmetries and Perturbations
Gurfil, P; Tangren, W; Efroimsky, M; Gurfil, Pini; Elipe, Antonio; Tangren, William; Efroimsky, Michael
2006-01-01
This paper reviews the Serret-Andoyer (SA) canonical formalism in rigid-body dynamics and presents some new results. As well known, the problem of unsupported and unperturbed rigid rotator can be reduced. The availability of this reduction is offered by the underlying symmetry, which stems from conservation of the angular momentum and rotational kinetic energy. When a perturbation is turned on, these quantities are no longer preserved. Nonetheless, the language of reduced description remains extremely instrumental even in the perturbed case. We describe the canonical reduction performed by the Serret-Andoyer (SA) method, and discuss its applications to attitude dynamics and to the theory of planetary rotation. Specifically, we consider the case of angular-velocity-dependent torques, and discuss the variation-of-parameters inherent antinomy between canonicity and osculation. Finally, we address the transformation of the Andoyer variables into the action-angle ones, using the method of Sadov.
A simplified impact stress analysis of dynamic systems which consist of elastic and rigid bodies
A simplified simulation technique is described for the impact stress analysis of elastic bodies which contain rigid bodies, as in the case of stacked nuclear waste storage canisters. A numerical method based on Guyan's static condensation is proposed which neglects coupling mass terms between rigid and elastic bodies. Modal analytical theory shows that the accuracy of this new method depends on the minimum modal mass ratio (MMMR) between elastic bodies and an induced equivalent mass-spring system, that is, a simplified system which assumes a linear displacement field. For systems with MMMR values greater than 5, this new technique yields results close to those of the more complicated Finite Element Method which requires a considerable computation time. It is a simple and inexpensive way to analyze complex elastic systems which include many rigid parts. (author)
Higher order coupling between rigid-body and elastic motion in flexible mechanisms
The paper presents an investigation of the influence of the higher order coupling terms between the rigid-body and elastic motion into flexible mechanism dynamics. The configuration of the mechanical system is obtained by using the so called hybrid coordinates. The kinematic description of the mechanism was obtained using the D-H 4 x 4 transformation matrices. The elastic deformation of each point of the mechanism is described by the finite element modeling (FEM) type interpolation scheme. The dynamic model of the flexible mechanism consists due to the hybrid coordinates of two groups of differential equations. The first group describes the manipulator transport motion and the second group describes the vibration. In this paper the authors evaluated the contribution of the coupling terms between the two groups of differential equations and selected only those with high contribution
The problem of exact interior solutions for rotating rigid bodies in general relativity
Wahlquist, H. D.
1993-01-01
The (3 + 1) dyadic formalism for timelike congruences is applied to derive interior solutions for stationary, axisymmetric, rigidly rotating bodies. In this approach the mathematics is formulated in terms of three-space-covariant, first-order, vector-dyadic, differential equations for a and Omega, the acceleration and angular velocity three-vectors of the rigid body; for T, the stress dyadic of the matter; and for A and B, the 'electric' and 'magnetic' Weyl curvature dyadics which describe the gravitational field. It is shown how an appropriate ansatz for the forms of these dyadics can be used to discover exact rotating interior solutions such as the perfect fluid solution first published in 1968. By incorporating anisotropic stresses, a generalization is found of that previous solution and, in addition, a very simple new solution that can only exist in toroidal configurations.
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
The Dynamics of a Rigid Body in Potential Flow with Circulation
Vankerschaver, Joris; Marsden, Jerrold E
2010-01-01
We consider the motion of a two-dimensional body of arbitrary shape in a planar irrotational, incompressible fluid with a given amount of circulation around the body. We derive the equations of motion for this system by performing symplectic reduction with respect to the group of volume-preserving diffeomorphisms and obtain the relevant Poisson structures after a further Poisson reduction with respect to the group of translations and rotations. In this way, we recover the equations of motion given for this system by Chaplygin and Lamb, and we give a geometric interpretation for the Kutta-Zhukowski force as a curvature-related effect. In addition, we show that the motion of a rigid body with circulation can be understood as a geodesic flow on a central extension of the special Euclidian group SE(2), and we relate the cocycle in the description of this central extension to a certain curvature tensor.
The numerical method for three-dimensional impact with friction of multi-rigid-body system
无
2006-01-01
The differential equations for planar impacts reduce to an algebraic form, and can be easily solved. For three dimensional impacts with friction, there is no closed-form solution, and numerical integration is required due to the swerve behavior of tangential impulse during collisions. The dynamic governing equations in the impact process are built up in impulse space based on the Lagrangian equation in this paper. The coefficient of restitution defined by Poisson is used as the condition of impact termination. A valid numerical method for solving three-dimensional frictional impact of multi-rigid body system is established. The singular cases of tangential movement in sticking point are especially noticed and analyzed. Several examples are present to reveal the different kinds of tangential movement modes varied with the normal impulse during collision.
Asymptotic of 'rigid-body' motions for nonlinear dynamics: physical insight and methodologies
Pilipchuk, V N
2014-01-01
The purpose of the present work is to show that an adequate basis for understanding the essentially nonlinear phenomena must also be essentially nonlinear however still simple enough to play the role of a basis. It is shown that such types of 'elementary' nonlinear models can be revealed by tracking the hidden links between analytical tools of analyses and subgroups of the rigid-body motions or, in other terms, rigid Euclidean transformation. While the subgroup of rotations is linked with linear and weakly nonlinear vibrations, the translations with reflections can be viewed as a geometrical core of the strongly nonlinear dynamics associated with the so-called vibro-impact behaviors. It is shown that the corresponding analytical approach develops through non-smooth temporal substitutions generated by the impact models.
Coupling Linear Sloshing with Six Degrees of Freedom Rigid Body Dynamics
Dubois, François
2014-01-01
Fluid motion in tanks is usually described in space industry with the so-called Lomen hypothesis which assumes the vorticity is null in the moving frame. We establish in this contribution that this hypothesis is valid only for uniform rotational motions. We give a more general formulation of this coupling problem, with a compact formulation. We consider the mechanical modelling of a rigid body with a motion of small amplitude, containing an incompressible fluid in the linearized regime. We first establish that the fluid motion remains irrotational in a Galilean referential if it is true at the initial time. When continuity of normal velocity and pressure are prescribed on the free surface, we establish that the global coupled problem conserve an energy functional composed by three terms. We introduce the Stokes - Zhukovsky vector fields, solving Neumann problems for the Laplace operator in the fluid in order to represent the rotational rigid motion with irrotational vector fields. Then we have a good framewor...
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 in...... microdimensions is investigated by changing the relative stiffness of the flexible beams. The actuation force versus displacement characteristics of several cases is explored and the full simulation results of one of the cases are presented. This paper demonstrates the united application of the PRBM and the...
In silico single-molecule manipulation of DNA with rigid body dynamics.
Pascal Carrivain
2014-02-01
Full Text Available We develop a new powerful method to reproduce in silico single-molecule manipulation experiments. We demonstrate that flexible polymers such as DNA can be simulated using rigid body dynamics thanks to an original implementation of Langevin dynamics in an open source library called Open Dynamics Engine. We moreover implement a global thermostat which accelerates the simulation sampling by two orders of magnitude. We reproduce force-extension as well as rotation-extension curves of reference experimental studies. Finally, we extend the model to simulations where the control parameter is no longer the torsional strain but instead the torque, and predict the expected behavior for this case which is particularly challenging theoretically and experimentally.
In silico single-molecule manipulation of DNA with rigid body dynamics.
Carrivain, Pascal; Barbi, Maria; Victor, Jean-Marc
2014-02-01
We develop a new powerful method to reproduce in silico single-molecule manipulation experiments. We demonstrate that flexible polymers such as DNA can be simulated using rigid body dynamics thanks to an original implementation of Langevin dynamics in an open source library called Open Dynamics Engine. We moreover implement a global thermostat which accelerates the simulation sampling by two orders of magnitude. We reproduce force-extension as well as rotation-extension curves of reference experimental studies. Finally, we extend the model to simulations where the control parameter is no longer the torsional strain but instead the torque, and predict the expected behavior for this case which is particularly challenging theoretically and experimentally. PMID:24586127
Weng, Shengxuan; Yue, Dong
2016-02-01
In this note, the distributed event-triggered cooperative attitude control of multiple rigid bodies with leader-follower architecture is investigated, where both the cases of static and dynamic leaders are all considered. Two distributed triggering procedures are first introduced for the followers and leaders, and then the distributed cooperative controllers are designed under the proposed triggering schemes. Under the designed controllers with the event-triggered strategies, it is shown that the orientations of followers converge to the convex hull formed by the desired leaders' orientations with zero angular velocities. Moreover, the communication pressure in network is reduced and the energy of each agent is saved. Simulation results show the effectiveness of the proposed method.
DYNAMIC BUCKLING OF ELASTIC-PLASTIC COLUMN IMPACTED BY RIGID BODY
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.
A Computational Model for Suspended Large Rigid Bodies in 3D Unsteady Viscous Flows
Xiao, Feng
1999-11-01
A 3D numerical model for computing large rigid objects suspended in fluid flow has been developed. Rather than calculating the surface pressure upon the solid body, we evaluate the net force and torque based on a volume force formulation. The total effective force is obtained by summing up the forces at the Eulerian grids occupied by the rigid body. The effects of the moving bodies are coupled to the fluid flow by imposing the velocity field of the bodies to the fluid. A Poisson equation is used to compute the pressure over the whole domain. The objects are identified by color functions and calculated by the PPM scheme and a tangent function transformation which scales the transition region of the computed interface to a compact thickness. The model is then implemented on a parallel computer of distributed memory and validated with Stokes and low Reynolds number flows.
On potential energies and constraints in the dynamics of rigid bodies and particles
O'reilly Oliver M.
2002-01-01
Full Text Available A new treatment of kinematical constraints and potential energies arising in the dynamics of systems of rigid bodies and particles is presented which is suited to Newtonian and Lagrangian formulations. Its novel feature is the imposing of invariance requirements on the constraint functions and potential energy functions. These requirements are extensively used in continuum mechanics and, in the present context, one finds certain generalizations of Newton's third law of motion and an elucidation of the nature of constraint forces and moments. One motivation for such a treatment can be found by considering approaches where invariance requirements are ignored. In contrast to the treatment presented in this paper, it is shown that this may lead to a difficulty in formulating the equations governing the motion of the system.
On docking, scoring and assessing protein-DNA complexes in a rigid-body framework.
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.
Slaughter, Chris; Yang, Allen Y.; 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 ...
C. Aguilar-Ibáñez; M.S. Suárez-Castañón; F. Guzmán-Aguilar
2008-01-01
We present a Hamiltonian control approach for the stabilization of a rigid body system that is controlled by two torques. The stabilization strategy consists in solving a feasible matching condition in order to derive a feedback controller which forces the closed-loop system to be globally asymptotically stable.
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.
A navigator-based rigid body motion correction for magnetic resonance imaging
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.
Application of rigid-body-spring-model to modeling of ultimate behavior of piping systems
When piping systems of nuclear power plants are subjected to large deformation during earthquakes, plasticity tends to concentrate at local elements such as elbows, tees and supports. In analyzing responses of such structures, it is effective to clearly divide them into those plastic parts and other linear parts. The rigid-body-spring-model (RBSM) is a structural analysis method which is effective in representing such discretely nonlinear systems. In order to apply RBSM for this purpose, load-displacement relations of the local plastic parts have to be determined, and it can be established by structural experiments of those independent elements. In this study, the authors conducted cyclic in-plane bending experiments of thin-walled elbows, and determined their asymmetric load-displacement relations by using the Ramberg-Osgood model and empirical hysteresis curves. Then, they are incorporated into nonlinear spring model of RBSM, which could accurately simulate the complex hysteresis loops observed in the experiments. Finally, the authors proposed a framework of limit-state seismic evaluation procedure for nuclear piping systems which uses RBSM and experimentally-determined load-displacement relations of pipe elements. Refs. 2 (author)
Inertial Motions of a Rigid Body with a Cavity Filled with a Viscous Liquid
Disser, Karoline; Galdi, Giovanni P.; Mazzone, Giusy; Zunino, Paolo
2016-07-01
We study inertial motions of the coupled system, {S}, constituted by a rigid body containing a cavity entirely filled with a viscous liquid. We show that for arbitrary initial data having only finite kinetic energy, every corresponding weak solution (à la Leray-Hopf) converges, as time goes to infinity, to a uniform rotation, unless two central moments of inertia of {S} coincide and are strictly greater than the third one. This corroborates a famous "conjecture" of N.Ye. Zhukovskii in several physically relevant cases. Moreover, we show that, in a known range of initial data, this rotation may only occur along the central axis of inertia of {S} with the larger moment of inertia. We also provide necessary and sufficient conditions for the rigorous nonlinear stability of permanent rotations, which improve and/or generalize results previously given by other authors under different types of approximation. Finally, we present results obtained by a targeted numerical simulation that, on the one hand, complement the analytical findings, whereas, on the other hand, point out new features that the analysis is yet not able to catch, and, as such, lay the foundation for interesting and challenging future investigation.
A navigator-based rigid body motion correction for magnetic resonance imaging
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.
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. PMID:19928105
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. PMID:26800289
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
On the orbital stability of pendulum-like vibrations of a rigid body carrying a rotor
Yehia, Hamad M.; El-Hadidy, E. G.
2013-09-01
One of the most notable effects in mechanics is the stabilization of the unstable upper equilibrium position of a symmetric body fixed from one point on its axis of symmetry, either by giving the body a suitable angular velocity or by adding a suitably spinned rotor along its axis. This effect is widely used in technology and in space dynamics. The aim of the present article is to explore the effect of the presence of a rotor on a simple periodic motion of the rigid body and its motion as a physical pendulum. The equation in the variation for pendulum vibrations takes the form in which α depends on the moments of inertia, ρ on the gyrostatic momentum of the rotor and ν (the modulus of the elliptic function) depends on the total energy of the motion. This equation, which reduces to Lame's equation when ρ = 0, has not been studied to any extent in the literature. The determination of the zones of stability and instability of plane motion reduces to finding conditions for the existence of primitive periodic solutions (with periods 4 K( ν), 8 K( ν)) with those parameters. Complete analysis of primitive periodic solutions of this equation is performed analogously to that of Ince for Lame's equation. Zones of stability and instability are determined analytically and illustrated in a graphical form by plotting surfaces separating them in the three-dimensional space of parameters. The problem is also solved numerically in certain regions of the parameter space, and results are compared to analytical ones.
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 ...
Wu, Tse-Huai; Lee, Taeyoung
2015-01-01
This paper studies a rigid body attitude tracking control problem with attitude measurements only, when angular velocity measurements are not available. An angular velocity observer is constructed such that the estimated angular velocity is guaranteed to converge to the true angular velocity asymptotically from almost all initial estimates. As it is developed directly on the special orthogonal group, it completely avoids singularities, complexities, or discontinuities caused by minimal attitu...
New solvable problems in the dynamics of a rigid body about a fixed point in a potential field
Yehia, Hamad M.
2013-01-01
We determine the general form of the potential of the problem of motion of a rigid body about a fixed point, which allows the angular velocity to remain permanently in a principal plane of inertia of the body. Explicit solution of the problem of motion is reduced to inversion of a single integral. A several-parameter generalization of the classical case due to Bobylev and Steklov is found. Special cases solvable in elliptic and ultraelliptic functions of time are discussed.
Marcello Romano
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 ...
Romano, Marcello
2008-08-01
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 ellipsoid of inertia. In particular, by following Hestenes’ theory, the rotational motion of an axially symmetric rigid body is seen at any instant in time as the combination of the motion of a “virtual” spherical body with respect to the inertial frame and the motion of the axially symmetric body with respect to this “virtual” body. The kinematic solutions are presented in terms of the rotation matrix. The newly found exact analytic solutions are valid for any motion time length and rotation amplitude. The present paper adds further elements to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.
Lohr, M. B.
2008-10-01
The rotational motion of a torque-free axisymmetric rigid body is precession. This motion has been expressed analytically in the literature given the body's initial orientation and rotational dynamics parameters, i.e. inertia ratio and initial angular velocities or precession parameters. The inverse problem of deriving these dynamics parameters given orientation in time has been implemented numerically but has not yet been solved analytically. If a rigid body is precessing, and its orientation with respect to an arbitrary inertial frame is provided at three equally spaced points in time such that the rotational motion is not undersampled, an analytical inverse solution is presented for the precession rate, relative spin rate, coning angle and angular velocities; if the precessional motion is due to inertial axisymmetry and torque-free motion, the inertia ratio is also derived. Additionally, an analytical methodology is presented to test for non-precessional motion. These techniques are applicable to various problems in space science and astronomy, where non-precessional motion or the rotational dynamics parameters of this type of rigid body must be accurately derived from its orientation or relative orientation in time.
Lācis, Uǧis; Taira, Kunihiko; Bagheri, Shervin
2016-01-01
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. Similarly 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 implicit coupling yields stable solution for density ratios as low as 10-4. We also consider the influence of fictitious fluid located inside the rigid bodies on the accuracy and stability of our method.
The rotational motion of a torque-free axisymmetric rigid body is precession. This motion has been expressed analytically in the literature given the body's initial orientation and rotational dynamics parameters, i.e. inertia ratio and initial angular velocities or precession parameters. The inverse problem of deriving these dynamics parameters given orientation in time has been implemented numerically but has not yet been solved analytically. If a rigid body is precessing, and its orientation with respect to an arbitrary inertial frame is provided at three equally spaced points in time such that the rotational motion is not undersampled, an analytical inverse solution is presented for the precession rate, relative spin rate, coning angle and angular velocities; if the precessional motion is due to inertial axisymmetry and torque-free motion, the inertia ratio is also derived. Additionally, an analytical methodology is presented to test for non-precessional motion. These techniques are applicable to various problems in space science and astronomy, where non-precessional motion or the rotational dynamics parameters of this type of rigid body must be accurately derived from its orientation or relative orientation in time
Multiple-Zone Diffractive Optic Element for Laser Ranging Applications
Ramos-Izquierdo, Luis A.
2011-01-01
A diffractive optic element (DOE) can be used as a beam splitter to generate multiple laser beams from a single input laser beam. This technology has been recently used in LRO s Lunar Orbiter Laser Altimeter (LOLA) instrument to generate five laser beams that measure the lunar topography from a 50-km nominal mapping orbit (see figure). An extension of this approach is to use a multiple-zone DOE to allow a laser altimeter instrument to operate over a wider range of distances. In particular, a multiple-zone DOE could be used for applications that require both mapping and landing on a planetary body. In this case, the laser altimeter operating range would need to extend from several hundred kilometers down to a few meters. The innovator was recently involved in an investigation how to modify the LOLA instrument for the OSIRIS asteroid mapping and sample return mission. One approach is to replace the DOE in the LOLA laser beam expander assembly with a multiple-zone DOE that would allow for the simultaneous illumination of the asteroid with mapping and landing laser beams. The proposed OSIRIS multiple-zone DOE would generate the same LOLA five-beam output pattern for high-altitude topographic mapping, but would simultaneously generate a wide divergence angle beam using a small portion of the total laser energy for the approach and landing portion of the mission. Only a few percent of the total laser energy is required for approach and landing operations as the return signal increases as the inverse square of the ranging height. A wide divergence beam could be implemented by making the center of the DOE a diffractive or refractive negative lens. The beam energy and beam divergence characteristics of a multiple-zone DOE could be easily tailored to meet the requirements of other missions that require laser ranging data. Current single-zone DOE lithographic manufacturing techniques could also be used to fabricate a multiple-zone DOE by masking the different DOE zones during
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.
This paper presents an algorithm for the efficient numerical analysis and simulation of modest to heavily constrained multi-rigid-body dynamic systems. The algorithm can accommodate the spatial motion of general multi-rigid-body systems containing arbitrarily many closed loops in O(n + m)operations overall for systems containing n generalized coordinates, and m independent algebraic constraints. The presented approach does not suffer from the performance (speed) penalty encountered by most other of the so-called 'O(n)' state-space formulations, when dealing with constraints which tend to actually show O(n + m + nm + nm2+ m3) performance. Additionally, these latter formulations may require additional constraint violation stabilization procedures (e.g. Baumgarte's method, coordinate partitioning, etc.) which can contribute significant additional computation. The presented method suffers less from this difficulty because the loop closure constraints at both the velocity and acceleration level are directly embedded within the formulation. Due to these characteristics, the presented algorithm offers superior computing performance relative to other methods in situations involving both large n and m
Ikuru Otomo
2014-04-01
Full Text Available In the field of design and manufacturing, there are many problems with managing dynamic states of three-dimensional (3D objects. In order to solve these problems, the four-dimensional (4D mesh model and its modeling system have been proposed. The 4D mesh model is defined as a 4D object model that is bounded by tetrahedral cells, and can represent spatio-temporal changes of a 3D object continuously. The 4D mesh model helps to solve dynamic problems of 3D models as geometric problems. However, the construction of the 4D mesh model is limited on the time-series 3D voxel data based method. This method is memory-hogging and requires much computing time. In this research, we propose a new method of constructing the 4D mesh model that derives from the 3D mesh model with continuous rigid body movement. This method is realized by making a swept shape of a 3D mesh model in the fourth dimension and its tetrahe-dralization. Here, the rigid body movement is a screwed movement, which is a combination of translational and rotational movement.
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...
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...
Mass of Rigid Body Real-Time Simulation on GPUs%基于GPU实现的大量刚体运动实时仿真
彭林春; 杨红雨; 杨光
2013-01-01
针对存在大量刚体运动的虚拟场景,提出一种基于在GPU上实现的实时仿真算法,利用GPU的并行计算能力,实时处理刚体交互,更新刚体状态.使用深度剥离技术,离散化刚体,并使其由一组具有相同大小的粒子表示.每一帧刚体间的运动交互则由粒子间的运动交互来实现.碰撞粒子对间的交互则用离散元法.通过统一网格方式,分割仿真域空间,以提高碰撞检测速率.实验证明,提出的新算法大幅度的提升了仿真大量刚体的速率.%In view of virtual scene where exist a mass of moving rigid bodies, we proposed a real - time rigid body simulation algorithm on CPU. This algorithm handles rigid body's interaction and status in real -time, utilizing the tremendous computational power provided by GPUs. We discretized rigid body using depth peeling, to making rigid body represented by a set of particles with the same size. We utilized particle pairs' interaction to realizing rigid body's interaction. Discrete element method was used to handle collision detection. And we discretized simulation areas across uniform grid to improve collision detection. The results show that this algorithm can improve the rigid body simulation speed largely.
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
Ershkov, Sergey V
2014-01-01
Here is presented a new exact solution of Euler's equations (rigid body dynamics, non-zero applied torques) in the case of reduction one of Euler's equations to a proper Abel ordinary differential equation. One component of angular velocity of rigid body for such a solution - is a proper classical solution for the case of symmetric rigid rotor (which has two equal moments of inertia), but applied torques is not zero. The 2-nd component is proved to be appropriate solution of Abel ordinary differential equation. Due to a very special character of Riccati's type equation (such as Abel ODE), its general solution is known to have a proper gap of above component of angular velocity of rigid body. It means a possibility of sudden acceleration of rigid body rotation around appropriate principal axe at definite moment of parametrical time. The 3-d could be obtained from a simple algebraic equality. It is a multiplying all the components of angular velocity of rigid body (which is to be a constant for such a solution)...
Wu, Shunguang; Hong, Lang
2008-04-01
A framework of simultaneously estimating the motion and structure parameters of a 3D object by using high range resolution (HRR) and ground moving target indicator (GMTI) measurements with template information is given. By decoupling the motion and structure information and employing rigid-body constraints, we have developed the kinematic and measurement equations of the problem. Since the kinematic system is unobservable by using only one scan HRR and GMTI measurements, we designed an architecture to run the motion and structure filters in parallel by using multi-scan measurements. Moreover, to improve the estimation accuracy in large noise and/or false alarm environments, an interacting multi-template joint tracking (IMTJT) algorithm is proposed. Simulation results have shown that the averaged root mean square errors for both motion and structure state vectors have been significantly reduced by using the template information.
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.
Rotation of the Earth as a Triaxial Rigid Body%三轴刚性地球体的旋转
申文斌; 陈巍; 王文均; 梁毅强
2007-01-01
The Earth is taken as a triaxial rigid body, which rotates freely in the Euclidian space. The starting equations are the Euler dynamic equations, with A smaller than B and B smaller than C. The Euler equations are solved, and the numerical results are provided. In the calculations, the following parameters are used: (C-B)/A=0.003 273 53; (B-A)/C=0.000 021 96:(C-A)/B=0.003 295 49, and the mean angular velocity of the Earth's rotation, ω =0.000 072 921 15 rad/s. Calculations show that, besides the self-rotation of the Earth and the free Euler procession of its rotation, there exists the free nutation:the nutation angle, or the angle between the Earth's momentary rotation axis and the mean axis that periodically change with time. The free nutation is investigated.
Knowledge-in-action: a study on the integration of forces and energy in a rigid body
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.
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.
Cardou, Philippe, E-mail: pcardou@cim.mcgill.ca; Angeles, Jorge [McGill University, Macdonald Engineering Building, Department of Mechanical Engineering, Centre for Intelligent Machines (Canada)
2008-05-15
Two methods are available for the estimation of the angular velocity of a rigid body from point-acceleration measurements: (i) the time-integration of the angular acceleration and (ii) the square-rooting of the centripetal acceleration. The inaccuracy of the first method is due mainly to the accumulation of the error on the angular acceleration throughout the time-integration process, which does not prevent that it be used successfully in crash tests with dummies, since these experiments never last more than one second. On the other hand, the error resulting from the second method is stable through time, but becomes inaccurate whenever the rigid body angular velocity approaches zero, which occurs in many applications. In order to take advantage of the complementarity of these two methods, a fusion of their estimates is proposed. To this end, the accelerometer measurements are modeled as exact signals contaminated with bias errors and Gaussian white noise. The relations between the variables at stake are written in the form of a nonlinear state-space system in which the angular velocity and the angular acceleration are state variables. Consequently, a minimum-variance-error estimate of the state vector is obtained by means of extended Kalman filtering. The performance of the proposed estimation method is assessed by means of simulation. Apparently, the resulting estimation method is more robust than the existing accelerometer-only methods and competitive with gyroscope measurements. Moreover, it allows the identification and the compensation of any bias error in the accelerometer measurements, which is a significant advantage over gyroscopes.
Two methods are available for the estimation of the angular velocity of a rigid body from point-acceleration measurements: (i) the time-integration of the angular acceleration and (ii) the square-rooting of the centripetal acceleration. The inaccuracy of the first method is due mainly to the accumulation of the error on the angular acceleration throughout the time-integration process, which does not prevent that it be used successfully in crash tests with dummies, since these experiments never last more than one second. On the other hand, the error resulting from the second method is stable through time, but becomes inaccurate whenever the rigid body angular velocity approaches zero, which occurs in many applications. In order to take advantage of the complementarity of these two methods, a fusion of their estimates is proposed. To this end, the accelerometer measurements are modeled as exact signals contaminated with bias errors and Gaussian white noise. The relations between the variables at stake are written in the form of a nonlinear state-space system in which the angular velocity and the angular acceleration are state variables. Consequently, a minimum-variance-error estimate of the state vector is obtained by means of extended Kalman filtering. The performance of the proposed estimation method is assessed by means of simulation. Apparently, the resulting estimation method is more robust than the existing accelerometer-only methods and competitive with gyroscope measurements. Moreover, it allows the identification and the compensation of any bias error in the accelerometer measurements, which is a significant advantage over gyroscopes
Multiple zone power forwards. A value at risk framework
Over the 1990s, deregulated power markets in New-England provided zones with fluctuating spot prices. Such prices have a notoriously high volatility, owing to the difficulty of storing electrical energy and the delays needed to adjust generation levels. In this context, forward contracts have become increasingly popular and understanding their dynamic is a problem facing many market players. This paper proposes a parsimonious parametric model, based on the price series of all n-month forward contracts (n = 1,2,3..), encompassing multiple zones. The model is then used for value at risk forecasts, which are backtested and compared with the ones in use by the risk management unit of an important electricity producer. Extensions to include natural gas and power-relevant oil-based future markets are discussed. (author)
Nagasaka, Imao; Ishida, Yukio; Koyama, Takayuki; Fujimatsu, Naoki
Currently, some kinds of helicopters use pendulum absorbers in order to reduce vibrations. Present pendulum absorbers are designed based on the antiresonance concept used in the linear theory. However, since the vibration amplitudes of the pendulum are not small, it is considered that the nonlinearity has influence on the vibration characteristics. Therefore, the best suppression cannot be attained by using the linear theory. In a helicopter, periodic forces act on the blades due to the influences of the air thrust. These periodic forces act on the blades with the frequency which is the integer multiple of the rotational speed of the rotor. Our previous study proposed a 2-degree-of-freedom (2DOF) model composed of a rotor blade and a pendulum absorber. The blade was considered as a rigid body and it was excited by giving a sinusoidal deflection at its end. The present paper proposes a 3DOF model that is more similar to the real helicopter, since the freedom of the fuselage is added and the periodic forces are applied to the blade by aerodynamic force. The vibration is analyzed considering the nonlinear characteristics. The resonance curves of rotor blades with pendulum absorbers are obtained analytically and experimentally. It is clarified that the most efficient condition is obtained when the natural frequency of the pendulum is a little bit different from the frequency of the external force. Various unique nonlinear characteristics, such as bifurcations, are also shown.
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.
Feng, Bing; Gifford, Howard C.; Beach, Richard D.; Boening, Guido; Gennert, Michael A.; King, Michael A.
2006-01-01
Due to the extended imaging times employed in SPECT and PET, patient motion during imaging is a common clinical occurrence. The fast and accurate correction of the three-dimensional (3D) translational and rotational patient motion in iterative reconstruction is thus necessary to address this important cause of artifacts. We propose a method of incorporating 3D Gaussian interpolation in the projector/backprojector pair to facilitate compensation for rigid-body motion in addition to attenuation...
Feng, Bing; King, Michael A.
2006-01-01
We developed a unique method for estimating and compensating rigid-body translations and rotations from scatter and-attenuation-compensated projection data in iterative reconstruction when multiple projection angles are acquired at the same time. During reconstruction, both the non-attenuated and attenuated line-integrals are calculated. Their ratios are then multiplied to the scatter-corrected projection data to estimate scatter-and-attenuation- compensated projection data. At the end of eac...
Romano, Marcello
2008-01-01
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 velocity 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 poi...
Nečasová, Šárka; Wolf, J.
2016-01-01
Roč. 36, č. 3 (2016), s. 1539-1562. ISSN 1078-0947 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : incompressible fluid * motion of rigid body * strong solutions Subject RIV: BA - General Mathematics Impact factor: 0.826, year: 2014 http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=11589
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.
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
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
Romano, Marcello
2008-03-01
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 motion time length and rotation amplitude. The present paper adds a further element to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.
Pathak, Ashish; Raessi, Mehdi
2014-11-01
We present a 3D MPI-parallel, GPU-accelerated computational tool that captures the interaction between a moving rigid body and two-fluid flows. Although the immediate application is the study of ocean wave energy converters (WECs), the model was developed at a general level and can be used in other applications. Solving the full Navier-Stokes equations, the model is able to capture non-linear effects, including wave-breaking and fluid-structure interaction, that have significant impact on WEC performance. To transport mass and momentum, we use a consistent scheme that can handle large density ratios (e.g. air/water). We present a novel reconstruction scheme for resolving three-phase (solid-liquid-gas) cells in the volume-of-fluid context, where the fluid interface orientation is estimated via a minimization procedure, while imposing a contact angle. The reconstruction allows for accurate mass and momentum transport in the vicinity of three-phase cells. The fast-fictitious-domain method is used for capturing the interaction between a moving rigid body and two-fluid flow. The pressure Poisson solver is accelerated using GPUs in the MPI framework. We present results of an array of test cases devised to assess the performance and accuracy of the computational tool.
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...
van Zundert, G C P; Bonvin, A M J J
2016-08-01
Cryo-electron microscopy provides fascinating structural insight into large macromolecular machines at increasing detail. Despite significant advances in the field, the resolution of the resulting three-dimensional images is still typically insufficient for de novo model building. To bridge the resolution gap and give an atomic interpretation to the data, high-resolution models are typically placed into the density as rigid bodies. Unfortunately, this is often done manually using graphics software, a subjective method that can lead to over-interpretation of the data. A more objective approach is to perform an exhaustive cross-correlation-based search to fit subunits into the density. Here we show, using five experimental ribosome maps ranging in resolution from 5.5 to 6.9Å, that cross-correlation-based fitting is capable of successfully fitting subunits correctly in the density for over 90% of the cases. Importantly, we provide indicators for the reliability and ambiguity of a fit, using the Fisher z-transformation and its associated confidence intervals, giving a formal approach to identify over-interpreted regions in the density. In addition, we quantify the resolution requirement for a successful fit as a function of the subunit size. For larger subunits the resolution of the data can be down-filtered to 20Å while still retaining an unambiguous fit. We leverage this information through the use of multi-scale image pyramids to accelerate the search up to 30-fold on CPUs and 40-fold on GPUs at a negligible loss in success rate. We implemented this approach in our rigid-body fitting software PowerFit, which can be freely downloaded from https://github.com/haddocking/powerfit. PMID:27318041
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.
王瑾; 孙宁
2012-01-01
针对三维空间,提出了一种可以同时测量刚体9个惯性参数的新方法.利用气体静压轴承低速自由转动时其角速度是一个随时间衰减的单指数函数这一运动规律,测量物体绕任意的转动惯量,通过9次测量最终求出刚体的9个惯性参数.设计了一套物体惯性参数测量仪,该测量仪可以同时测量三维空间中物体的9个惯性参数.测量过程中无需重新装配,减少了中间测试量及人为干预误差,使测量时间缩短,测量精度提高.%For three-dimensional space, a new method which can measure the nine inertial parameters of a rigid body simultaneously is proposed. With the law of motion that when aerostatic bearing move slowly its angular velocity is a single exponential function decayed with time, the moment of inertia of the rigid body rotating a axis in an arbitrary direction is obtained, through nine measurements, the inertial parameters of a rigid body can be got finally. A set of instrument used for measuring the rigid body inertial parameters is designed. This instrument can measure the nine inertial parameters of a rigid body in three-dimensional space simultaneously. There' s no need to re-assembly in the process of measurement, so intermediate testing quantity, error made by human and measuring time are all reduced.
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.
McBride, Carl; Noya, Eva G.; Vega, Carlos
2013-03-01
Here we provide FORTRAN source code to facilitate the calculation of the “Noya-Vega-McBride” (NVM) rotational propagator for asymmetric tops [E.G. Noya, C. Vega, C. McBride, J. Chem. Phys. 134 (2011) 054117] for a given value of PT and A, B and C, where P is the number of beads, T is the temperature, and A, B and C are the rotational constants for the system in question. The resulting NVM propagator calculated by the code provided can then be used to obtain the quantum rotational energy during a path integral Monte Carlo simulation of rigid bodies. Catalogue identifier: AEOA_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEOA_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 624734 No. of bytes in distributed program, including test data, etc.: 9890026 Distribution format: tar.gz Programming language: Fortran. Computer: Any. Operating system: Any. RAM: code included in the distribution package). Nature of problem: Calculation of the NVM rotational propagator Solution method: Fortran implementation of the NVM propagator equation. Additional comments: Example and test calculations are provided. Running time: 2-200 hours. Two examples are provided. The PT_1497 example will take approximately 11 hours to run. The quick_test should only take a few minutes.
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.
李学相; 安学庆
2012-01-01
现有的非刚体三维运动重建算法很难根据不同的场景、不同的非刚体来寻找不同的形状基,这种情况对重建过程产生了很大的影响,造成模型失真.为了解决这一问题,提出一种基于Murkowski距离连续的非刚体三维运动恢复算法,该算法根据在高速分解的图像序列中帧与帧之间的运动参数与特征点位移变化都呈现连续平缓的物理特性,在Murkowski距离约束的情况下,将运动结构参数通过非线性优化的方法来进行求解,最终得到非刚体的三维运动结构,并且通过仿真实验,验证了它的可行.%The existing non rigid body three dimensional motion reconstruction algorithm is difficult to find different shapes according to different scene and different non rigid body mus,and this kind of situation will exert great influence on the reconstruction process,cause model distortion. In order to solve this problem, this paper put forward a murkowski distance based continuous non rigid body three dimensional movement recovery algorithm, which presents continuous physical characteristics on the decomposition of image sequence of frame and frame between the movement parameters and feature point displacement change. Using the physical characteristics will solve motion structure parameter in Murkowski range bound through the nonlinear optimization method, and get the non rigid body 3D motion structure, and the experiment shows that simulation verification results are feasible.
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.
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
Feng, Bing; King, Michael A
2006-11-01
We developed a unique method for estimating and compensating rigid-body translations and rotations from scatter and-attenuation-compensated projection data in iterative reconstruction when multiple projection angles are acquired at the same time. During reconstruction, both the non-attenuated and attenuated line-integrals are calculated. Their ratios are then multiplied to the scatter-corrected projection data to estimate scatter-and-attenuation- compensated projection data. At the end of each iteration, the sets of compensated projection data for the angles acquired at the same time are employed to calculate the center-of mass and the inertia tensor, which are used to estimate the location and orientation of the imaging object by the principle-axes method. The estimated motion is applied in the next iteration to reposition the estimated slices and attenuation map in the projector and back-projector to match the pose of the patient at time the projections were acquired. To evaluate our method, we simulated an acquisition of the MCAT phantom with a 3-head SPECT system and imaged the Data Spectrum anthropomorphic phantom on a 3-head IRIX SPECT system. In simulations the phantom translated and rotated by the same amount 9 times. A numerical projector modeling the motion, attenuation, and distance-dependent blurring was used to generate the projection data. Poisson noise was added and 30 noise-realizations were generated. In the experiment with the anthropomorphic phantom, four 360-degree acquisitions were performed with the phantom translated or rotated beforehand. A motion-present dataset was made by mixing the 4 acquisitions. For both the MCAT phantom simulations and anthropomorphic phantom experiment, the motion-present data were reconstructed with 10 iterations of the OSEM which estimates and corrects the motion as described above. Our method obtained visually artifact-free reconstructions, while the reconstruction with no motion correction showed severe artifacts
熊国华; 蔡建乐; 撒凤杰
2011-01-01
利用3DS MAX及Cult 3D软件操作平台,先建立三维虚拟的刚体转动实验仪器模型,再使用Cult 3D Designer编辑器,通过组织事件、动作与对象的关联编程,实现了该实验的复杂交互动作.完成基于交互式虚拟技术的刚体转动实验浏览与操纵系统.%The service platforms of 3DS MAX and Cult 3D software were used. Firstly, the dummy model of rotational rigid body experiment was made. Then the Cult 3D Designer editor was made use of to realize the complex interactive operation through programming the relevance among event, motion and object. Finally, the browse and manipulative system of rotational rigid body experiment, which is based on interactive VR technology, is completed.
Takayama, Yuki; Schwieters, Charles D.; Grishaev, Alexander; Ghirlando, Rodolfo; Clore, G. Marius (NIH)
2012-10-23
The first component of the bacterial phosphotransferase system, enzyme I (EI), is a multidomain 128 kDa dimer that undergoes large rigid-body conformational transitions during the course of its catalytic cycle. Here we investigate the solution structure of a non-phosphorylatable active-site mutant in which the active-site histidine is substituted by glutamine. We show that perturbations in the relative orientations and positions of the domains and subdomains can be rapidly and reliably determined by conjoined rigid-body/torsion angle/Cartesian simulated annealing calculations driven by orientational restraints from residual dipolar couplings and shape and translation information afforded by small- and wide-angle X-ray scattering. Although histidine and glutamine are isosteric, the conformational space available to a Gln side chain is larger than that for the imidazole ring of His. An additional hydrogen bond between the side chain of Gln189 located on the EIN{sup {alpha}/{beta}} subdomain and an aspartate (Asp129) on the EIN{sup {alpha}} subdomain results in a small ({approx}9{sup o}) reorientation of the EIN{sup {alpha}} and EIN{sup {alpha}/{beta}} subdomains that is in turn propagated to a larger reorientation ({approx}26{sup o}) of the EIN domain relative to the EIC dimerization domain, illustrating the positional sensitivity of the EIN domain and its constituent subdomains to small structural perturbations.
Development and characterization of an automatic technique for the alignment of fMRI time series.
Ciulla, C; Deek, F P
2001-01-01
An automatic technique for the registration of fMRI time series has been developed, implemented and tested. The method assumes the human brain to be a rigid body and computes a head coordinate system on the basis of three reference points that lies on the directions corresponding to two of the principal axes of the volume at the intersections with the head boundary. Such directions are found computing the eigenvectors of the symmetric inertia matrix of the image. The inertia components were extracted weighting pixels' coordinates with their intensity values. The three reference points were found in the same position, relative to the head, in both the test and the reference images. The technique has been tested using T2*-weighted Magnetic Resonance (MR) images in which known rigid body transformations have been applied. The results obtained indicate that the method offers subvoxel accuracy in correcting misalignment among time points in fMRI time series. PMID:11599532
Experimental investigation of a single-plane automatic balancing mechanism for a rigid rotor
Rodrigues, DJ; Champneys, AR; Friswell, MI; Wilson, RE
2010-01-01
We present an experimental investigation of a single-plane automatic balancer that is fitted to a rigid rotor. Two balls, which are free to travel around a circular race, are used to compensate for the mass imbalance in the plane of the device. The experimental rig possesses both cylindrical and conical rigid body modes and the performance of the automatic balancer is assessed for a variety of different levels of imbalance. A non-planar mathematical model that also includes the observed effec...
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.
The no-type curve with negative skin of a horizontal well has been found in the current research. Negative skin is very significant to transient well test and rate decline analysis. This paper first presents the negative skin problem where the type curves with negative skin of a horizontal well are oscillatory. In order to solve the problem, we propose a new model of transient well test and rate decline analysis for a horizontal well in a multiple-zone composite reservoir. A new dimensionless definition of rD is introduced in the dimensionless mathematical modelling under different boundaries. The model is solved using the Laplace transform and separation of variables techniques. In Laplace space, the solutions for both constant rate production and constant wellbore pressure production are expressed in a unified formula. We provide graphs and thorough analysis of the new standard type curves for both well test and rate decline analysis; the characteristics of type curves are the reflections of horizontal well production in a multiple-zone reservoir. An important contribution of our paper is that our model removed the oscillation in type curves and thus solved the negative skin problem. We also show that the characteristics of type curves depend heavily on the properties of different zones, skin factor, well length, formation thickness, etc. Our research can be applied to a real case study
用四元数描述飞行器姿态时的几个基本问题%The Key Problems of Describing Rigid-Body Attitude by Using Quaternion
范奎武
2012-01-01
讨论描述刚体空间姿态的欧拉—克雷洛夫角、方向余弦矩阵、四元数这三种方法,给出方向余弦矩阵与四元数之间关系的推导方法,推导并验证了合成转动四元数的求取方法,介绍了通过方向余弦矩阵推导四元数微分方程的方法.%The three methods of describing rigid-body spatial attitude by using Euler-krylov angle , direction cosine matrix and quaternion are discussed firstly, then the derivation of relationship between direction' cosine matrix and quaternion is presented, in which the algorithm method of resultant rotation quaternion is deduced and verified. Finally, the derivation method of quaternion differential equation by using direction cosine matrix is proposed in detail.
Rigid body essential X-ray crystallography
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...
The rigid body obliquity history of mars
The primary objective of this study is to explore the range of uncertainty in the obliquity history of Mars associated with the present uncertainty in the axial precession rate. The obliquity, or angular separation between the spin axis and the orbit normal, is the most important parameter for determining the seasonal and latitudinal pattern of insolation. Thus significant variations in obliquity are a likely source of major climatic variations on Mars. The present obliquity is well known, and the torques acting to reorient the spin axis of Mars can be readily calculated for time spans of order 107 years into the past (or future). The primary limitation to reconstructing the obliquity history is uncertainty in the mean moment of inertial of Mars, which governs its response to the applied torques. The range of axial precession rates corresponding to recent theoretical estimates of the moment of inertial is 8.29-8.77 arc sec/yr, but even the most recent observational limits are still much broader: 8-12 arc sec/yr. Nominal estimates of the axial precession rate suggest that resonant amplification of a number of small terms in the orbital inclination series will lead to significant variations in the obliquity of Mars, a behavior much different from the Earth. The major variations are on a 105 year time scale, with significant amplitude modulation on a 106 year time scale. Because of this resonant amplification, estimates of the obliquity history depend very sensitively on assumed values for the axial precession rate. Three different analytic techniques are applied to the obliquity problem. Both linear perturbation analysis and direct numerical integration of the governing differential equations can be used to obtain an obliquity time series, once a model value is selected for the moment of inertia
José E. O. Reges
2016-07-01
Full Text Available This work is a contribution to the development of flow sensors in the oil and gas industry. It presents a methodology to measure the flow rates into multiple-zone water-injection wells from fluid temperature profiles and estimate the measurement uncertainty. First, a method to iteratively calculate the zonal flow rates using the Ramey (exponential model was described. Next, this model was linearized to perform an uncertainty analysis. Then, a computer program to calculate the injected flow rates from experimental temperature profiles was developed. In the experimental part, a fluid temperature profile from a dual-zone water-injection well located in the Northeast Brazilian region was collected. Thus, calculated and measured flow rates were compared. The results proved that linearization error is negligible for practical purposes and the relative uncertainty increases as the flow rate decreases. The calculated values from both the Ramey and linear models were very close to the measured flow rates, presenting a difference of only 4.58 m³/d and 2.38 m³/d, respectively. Finally, the measurement uncertainties from the Ramey and linear models were equal to 1.22% and 1.40% (for injection zone 1; 10.47% and 9.88% (for injection zone 2. Therefore, the methodology was successfully validated and all objectives of this work were achieved.
Reges, José E O; Salazar, A O; Maitelli, Carla W S P; Carvalho, Lucas G; Britto, Ursula J B
2016-01-01
This work is a contribution to the development of flow sensors in the oil and gas industry. It presents a methodology to measure the flow rates into multiple-zone water-injection wells from fluid temperature profiles and estimate the measurement uncertainty. First, a method to iteratively calculate the zonal flow rates using the Ramey (exponential) model was described. Next, this model was linearized to perform an uncertainty analysis. Then, a computer program to calculate the injected flow rates from experimental temperature profiles was developed. In the experimental part, a fluid temperature profile from a dual-zone water-injection well located in the Northeast Brazilian region was collected. Thus, calculated and measured flow rates were compared. The results proved that linearization error is negligible for practical purposes and the relative uncertainty increases as the flow rate decreases. The calculated values from both the Ramey and linear models were very close to the measured flow rates, presenting a difference of only 4.58 m³/d and 2.38 m³/d, respectively. Finally, the measurement uncertainties from the Ramey and linear models were equal to 1.22% and 1.40% (for injection zone 1); 10.47% and 9.88% (for injection zone 2). Therefore, the methodology was successfully validated and all objectives of this work were achieved. PMID:27420068
Haeseler, Friedrich
2003-01-01
Automatic sequences are sequences which are produced by a finite automaton. Although they are not random they may look as being random. They are complicated, in the sense of not being not ultimately periodic, they may look rather complicated, in the sense that it may not be easy to name the rule by which the sequence is generated, however there exists a rule which generates the sequence. The concept automatic sequences has special applications in algebra, number theory, finite automata and formal languages, combinatorics on words. The text deals with different aspects of automatic sequences, in particular:· a general introduction to automatic sequences· the basic (combinatorial) properties of automatic sequences· the algebraic approach to automatic sequences· geometric objects related to automatic sequences.
Automatic registration of serial mammary gland sections
Arganda-Carreras, Ignacio; Fernandez-Gonzalez, Rodrigo; Ortiz-de-Solorzano, Carlos
2004-04-13
We present two new methods for automatic registration of microscope images of consecutive tissue sections. They represent two possibilities for the first step in the 3-D reconstruction of histological structures from serially sectioned tissue blocks. The goal is to accurately align the sections in order to place every relevant shape contained in each image in front of its corresponding shape in the following section before detecting the structures of interest and rendering them in 3D. This is accomplished by finding the best rigid body transformation (translation and rotation) of the image being registered by maximizing a matching function based on the image content correlation. The first method makes use of the entire image information, whereas the second one uses only the information located at specific sites, as determined by the segmentation of the most relevant tissue structures. To reduce computing time, we use a multiresolution pyramidal approach that reaches the best registration transformation in increasing resolution steps. In each step, a subsampled version of the images is used. Both methods rely on a binary image which is a thresholded version of the Sobel gradients of the image (first method) or a set of boundaries manually or automatically obtained that define important histological structures of the sections. Then distance-transform of the binary image is computed. A proximity function is then calculated between the distance image of the image being registered and that of the reference image. The transformation providing a maximum of the proximity function is then used as the starting point of the following step. This is iterated until the registration error lies below a minimum value.
Full text: Image registration is one source of uncertainty in image guided radiotherapy. The performance of masked, soft-tissue, automatic image registration of the prostate between CT and CBCT images was measured and its relationship with reduced imaging dose investigated. An anthropomorphic pelvis phantom (CIRS) was CT scanned and used as a reference for lGRT. Seven CBCT scans were taken using the Elekta Synergy system with nominal imaging doses from I to 40 mGy. Rigid-body image registration was repeated 100 times with randomly selected start positions representing normal prostate set-up errors. Image registration used the 'Elekta Correlation Ratio' algorithm with CT data masked to the prostate + 5 mm isotropic margin. Residual error analysis was performed to determine the registration accuracy, precision and robustness. Rigid body errors were analysed as target registration error (TRE), the average error between any two corresponding points on the surface of a 5 cm sphere centred on the isocentre. Similar methods were applied to 21 CBCT scans from seven patients. The TRE was stable for imaging doses above 6 mGy. Median(TRE) was 3.6 mm) was ation performance for patient images was highly variable; 4121 CT-CBCT registrations showed median(TRE) < I mm and RFF <20%. For the rest, median(TRE) was up to 9 mm and RFF from 20 to 90%. A clear dose response relationship was evident for CTCBCT image registration performance of the prostate in phantom measurements. Performance with patient images was highly variable.
Reorientation of Asymmetric Rigid Body Using Two Controls
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.
Reorientation of Asymmetric Rigid Body Using Two Controls
Donghoon Kim; Turner, James D.; Henzeh Leeghim
2013-01-01
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 th...
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....
Rigid-body molecular dynamics of DNA inside a nucleosome.
Fathizadeh, Arman; Berdy Besya, Azim; Reza Ejtehadi, Mohammad; Schiessel, Helmut
2013-03-01
The majority of eukaryotic DNA, about three quarter, is wrapped around histone proteins forming so-called nucleosomes. To study nucleosomal DNA we introduce a coarse-grained molecular dynamics model based on sequence-dependent harmonic rigid base pair step parameters of DNA and nucleosomal binding sites. Mixed parametrization based on all-atom molecular dynamics and crystallographic data of protein-DNA structures is used for the base pair step parameters. The binding site parameters are adjusted by experimental B-factor values of the nucleosome crystal structure. The model is then used to determine the energy cost for placing a twist defect into the nucleosomal DNA which allows us to use Kramers theory to calculate nucleosome sliding caused by such defects. It is shown that the twist defect scenario together with the sequence-dependent elasticity of DNA can explain the slow time scales observed for nucleosome mobility along DNA. With this method we also show how the twist defect mechanism leads to a higher mobility of DNA in the presence of sin mutations near the dyad axis. Finally, by performing simulations on 5s rDNA, 601, and telomeric base pair sequences, it is demonstrated that the current model is a powerful tool to predict nucleosome positioning. PMID:23475204
Hamiltonian Dynamics of Spider-Type Multirotor Rigid Bodies Systems
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.
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
Dynamic model for landsliding monitoring under rigid body assumption
朱建军; 丁晓利; 陈永奇
2001-01-01
Based on the assumption that the slope bodies are rigid, the dynamic model of the landsiding (forward model) was put forward. According to the dynamic model, the system equations of Kalman filter were constituted. The mechanical status of a slope was hence combined with the monitoring data by Kalman filter. The model uncertainties or model errors could also be considered through some fictitious observation equations. Different from existed methods, the presented method can make use for not only the statistic information contained in the data but also the information provided by the mechanical and geological aspect of slopes. At last a numerical example was given out to show the feasibility of the method.
Simulation Methods in the Contact with Impact of Rigid Bodies
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
Dynamics of Rigid Bodies and Flexible Beam Structures
Nielsen, Martin Bjerre; Krenk, Steen
2013-01-01
Roterende bevægelse er et ofte forekommende fænomen indenfor mange ingeniørmæssige anvendelser såsom biler, roterende maskineri og vindmøllerotorer. Denne afhandling består af fire dele, der alle omhandler udvikling af effektive beregningsmetoder til modellering af den dynamiske opførsel af stive legemer og fleksible bjælkekonstruktioner med hovedvægt på den roterende bevægelse. Den første del vedrører bevægelse i en roterende referenceramme. En ny fremgangsmåde, hvor bevægelsesligningerne er...
A generic detailed rigid-body lumbar spine model
De Zee, Mark; Hansen, Lone; Wong, Christian;
2007-01-01
The objective of this work is to present a musculo-skeletal model of the lumbar spine, which can be shared and lends itself to investigation in many locations by different researchers. This has the potential for greater reproducibility and subsequent improvement of its quality from the combined e...
Rigid body dynamics simulation for robot motion planning
Ettlin, Alan
2006-01-01
The development of robot motion planning algorithms is inherently a challenging task. This is more than ever true when the latest trends in motion planning are considered. Some motion planners can deal with kinematic and dynamic constraints induced by the mechanical structure of the robot. Another class of motion planners fulfill various types of optimality conditions, yet others include means of dealing with uncertainty about the robot and its environment. Sensor-based motion planners gather...
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...
Collisions of rigid bodies, deformable bodies and fluids
DIMNET, E; Fremond, M.; GORMAZ, R; San Martin, J.
2003-01-01
The system made of two solids is deformable because the relative position of the solids may change. This idea is applied to an old and complex problem of mechanics : the collision theory. The major findings are constitutive laws which are coherent from the thermodynamics point of view. They give robust and productive models and numerical methods, for instance for rocks avalanches and collisions of solids and flluids.
Quaternion Feedback Control for Rigid-body Spacecraft
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 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 ...
Hurricane Balls: A rigid-body-motion student project
Jackson, David; Mertens, David; Pearson, Brett
Hurricane Balls is a spinning-top toy that consists of two metal spheres that are welded (or glued) together. The motion of Hurricane Balls provides a beautiful example of rotational motion in which the angular velocity and angular momentum point in different directions. Because the motion is both captivating to students and extremely reproducible, this system is an ideal example to include in a classical mechanics course. Moreover, the excellent agreement between theory and experiment makes a detailed analysis of Hurricane Balls a perfect topic for an independent student project. This talk will give an overview of the system and will provide some tips on how to make such a project a successful student experience.
Dynamics of Rigid Bodies and Flexible Beam Structures
Nielsen, Martin Bjerre
quaternion parameters or nine convected base vector components. In both cases, the equations of motion are obtained via Hamilton’s equations by including the kinematic constraints associated with the redundant rotation description by means of Lagrange multipliers. A special feature of the formulation is that...
Quaternion Feedback Control for Rigid-body Spacecraft
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...
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....
Euler-Poincaré Reduction of a Rigid Body Motion
Wisniewski, Rafal; Kulczycki, P.
2004-01-01
If a mechanical system experiences symmetry, the Lagrangian becomes invariant under a certain group action. This property leads to substantial simplification of the description of movement. The standpoint in this article is a mechanical system affected by an external force of a control action. As...
Purpose: In X-ray fused with MRI, previously gathered roadmap MRI volume images are overlaid on live X-ray fluoroscopy images to help guide the clinician during an interventional procedure. The incorporation of MRI data allows for the visualization of soft tissue that is poorly visualized under X-ray. The widespread clinical use of this technique will require fully automating as many components as possible. While previous use of this method has required time-consuming manual intervention to register the two modalities, in this article, the authors present a fully automatic rigid-body registration method. Methods: External fiducial markers that are visible under these two complimentary imaging modalities were used to register the X-ray images with the roadmap MR images. The method has three components: (a) The identification of the 3D locations of the markers from a full 3D MR volume, (b) the identification of the 3D locations of the markers from a small number of 2D X-ray fluoroscopy images, and (c) finding the rigid-body transformation that registers the two point sets in the two modalities. For part (a), the localization of the markers from MR data, the MR volume image was thresholded, connected voxels were segmented and labeled, and the centroids of the connected components were computed. For part (b), the X-ray projection images, produced by an image intensifier, were first corrected for distortions. Binary mask images of the markers were created from the distortion-corrected X-ray projection images by applying edge detection, pattern recognition, and image morphological operations. The markers were localized in the X-ray frame using an iterative backprojection-based method which segments voxels in the volume of interest, discards false positives based on the previously computed edge-detected projections, and calculates the locations of the true markers as the centroids of the clusters of voxels that remain. For part (c), a variant of the iterative closest
Long, Fan; Ganesh, Vijay; Carbin, Michael James; Sidiroglou, Stelios; Rinard, Martin
2012-01-01
We present a novel technique, automatic input rectification, and a prototype implementation, SOAP. SOAP learns a set of constraints characterizing typical inputs that an application is highly likely to process correctly. When given an atypical input that does not satisfy these constraints, SOAP automatically rectifies the input (i.e., changes the input so that it satisfies the learned constraints). The goal is to automatically convert potentially dangerous inputs into typical inputs that the ...
Narcis Eduard Mitu
2013-11-01
Full Text Available Policies or institutions (built into an economic system that automatically tend to dampen economic cycle fluctuations in income, employment, etc., without direct government intervention. For example, in boom times, progressive income tax automatically reduces money supply as incomes and spendings rise. Similarly, in recessionary times, payment of unemployment benefits injects more money in the system and stimulates demand. Also called automatic stabilizers or built-in stabilizers.
Automatic differentiation bibliography
Corliss, G.F. (comp.)
1992-07-01
This is a bibliography of work related to automatic differentiation. Automatic differentiation is a technique for the fast, accurate propagation of derivative values using the chain rule. It is neither symbolic nor numeric. Automatic differentiation is a fundamental tool for scientific computation, with applications in optimization, nonlinear equations, nonlinear least squares approximation, stiff ordinary differential equation, partial differential equations, continuation methods, and sensitivity analysis. This report is an updated version of the bibliography which originally appeared in Automatic Differentiation of Algorithms: Theory, Implementation, and Application.
Automatic Implantable Cardiac Defibrillator
Full Text Available Automatic Implantable Cardiac Defibrillator February 19, 2009 Halifax Health Medical Center, Daytona Beach, FL Welcome to Halifax Health Daytona Beach, Florida. Over the next hour you' ...
Automatic Payroll Deposit System.
Davidson, D. B.
1979-01-01
The Automatic Payroll Deposit System in Yakima, Washington's Public School District No. 7, directly transmits each employee's salary amount for each pay period to a bank or other financial institution. (Author/MLF)
Leandro Martínez
Full Text Available The analysis of structural mobility in molecular dynamics plays a key role in data interpretation, particularly in the simulation of biomolecules. The most common mobility measures computed from simulations are the Root Mean Square Deviation (RMSD and Root Mean Square Fluctuations (RMSF of the structures. These are computed after the alignment of atomic coordinates in each trajectory step to a reference structure. This rigid-body alignment is not robust, in the sense that if a small portion of the structure is highly mobile, the RMSD and RMSF increase for all atoms, resulting possibly in poor quantification of the structural fluctuations and, often, to overlooking important fluctuations associated to biological function. The motivation of this work is to provide a robust measure of structural mobility that is practical, and easy to interpret. We propose a Low-Order-Value-Optimization (LOVO strategy for the robust alignment of the least mobile substructures in a simulation. These substructures are automatically identified by the method. The algorithm consists of the iterative superposition of the fraction of structure displaying the smallest displacements. Therefore, the least mobile substructures are identified, providing a clearer picture of the overall structural fluctuations. Examples are given to illustrate the interpretative advantages of this strategy. The software for performing the alignments was named MDLovoFit and it is available as free-software at: http://leandro.iqm.unicamp.br/mdlovofit.
A review of metaphase chromosome image selection techniques for automatic karyotype generation.
Arora, Tanvi; Dhir, Renu
2016-08-01
The karyotype is analyzed to detect the genetic abnormalities. It is generated by arranging the chromosomes after extracting them from the metaphase chromosome images. The chromosomes are non-rigid bodies that contain the genetic information of an individual. The metaphase chromosome image spread contains the chromosomes, but these chromosomes are not distinct bodies; they can either be individual chromosomes or be touching one another; they may be bent or even may be overlapping and thus forming a cluster of chromosomes. The extraction of chromosomes from these touching and overlapping chromosomes is a very tedious process. The segmentation of a random metaphase chromosome image may not give us correct and accurate results. Therefore, before taking up a metaphase chromosome image for analysis, it must be analyzed for the orientation of the chromosomes it contains. The various reported methods for metaphase chromosome image selection for automatic karyotype generation are compared in this paper. After analysis, it has been concluded that each metaphase chromosome image selection method has its advantages and disadvantages. PMID:26676686
Automatic Arabic Text Classification
Al-harbi, S; Almuhareb, A.; Al-Thubaity , A; Khorsheed, M. S.; Al-Rajeh, A.
2008-01-01
Automated document classification is an important text mining task especially with the rapid growth of the number of online documents present in Arabic language. Text classification aims to automatically assign the text to a predefined category based on linguistic features. Such a process has different useful applications including, but not restricted to, e-mail spam detection, web page content filtering, and automatic message routing. This paper presents the results of experiments on documen...
Automatic Program Development is a tribute to Robert Paige (1947-1999), our accomplished and respected colleague, and moreover our good friend, whose untimely passing was a loss to our academic and research community. We have collected the revised, updated versions of the papers published in his...... honor in the Higher-Order and Symbolic Computation Journal in the years 2003 and 2005. Among them there are two papers by Bob: (i) a retrospective view of his research lines, and (ii) a proposal for future studies in the area of the automatic program derivation. The book also includes some papers by...... members of the IFIP Working Group 2.1 of which Bob was an active member. All papers are related to some of the research interests of Bob and, in particular, to the transformational development of programs and their algorithmic derivation from formal specifications. Automatic Program Development offers a...
Smith, Colin Boughton [Energy Metering Technology (United Kingdom)
2000-08-01
At present, energy audits represent only snapshot situations of the flow of energy. The normal pattern of energy audits as seen through the eyes of an experienced energy auditor is described. A brief history of energy auditing is given. It is claimed that the future of energy auditing lies in automatic meter reading with expert data analysis providing continuous automatic auditing thereby reducing the skill element. Ultimately, it will be feasible to carry out auditing at intervals of say 30 minutes rather than five years.
Burelli, Paolo; Preuss, Mike
2014-01-01
Automatically generating computer animations is a challenging and complex problem with applications in games and film production. In this paper, we investigate howto translate a shot list for a virtual scene into a series of virtual camera configurations — i.e automatically controlling the virtual...... camera. We approach this problem by modelling it as a dynamic multi-objective optimisation problem and show how this metaphor allows a much richer expressiveness than a classical single objective approach. Finally, we showcase the application of a multi-objective evolutionary algorithm to generate a shot...
Torres Moreno, Juan Manuel
2014-01-01
This new textbook examines the motivations and the different algorithms for automatic document summarization (ADS). We performed a recent state of the art. The book shows the main problems of ADS, difficulties and the solutions provided by the community. It presents recent advances in ADS, as well as current applications and trends. The approaches are statistical, linguistic and symbolic. Several exemples are included in order to clarify the theoretical concepts. The books currently available in the area of Automatic Document Summarization are not recent. Powerful algorithms have been develop
Automatic Dance Lesson Generation
Yang, Yang; Leung, H.; Yue, Lihua; Deng, LiQun
2012-01-01
In this paper, an automatic lesson generation system is presented which is suitable in a learning-by-mimicking scenario where the learning objects can be represented as multiattribute time series data. The dance is used as an example in this paper to illustrate the idea. Given a dance motion sequence as the input, the proposed lesson generation…
Rosendahl, Mads
1989-01-01
One way to analyse programs is to to derive expressions for their computational behaviour. A time bound function (or worst-case complexity) gives an upper bound for the computation time as a function of the size of input. We describe a system to derive such time bounds automatically using abstract...
Automatic indexing, compiling and classification
A review of the principles of automatic indexing, is followed by a comparison and summing-up of work by the authors and by a Soviet staff from the Moscou INFORM-ELECTRO Institute. The mathematical and linguistic problems of the automatic building of thesaurus and automatic classification are examined
The paper describes the automatic gaussmeter operating according to the principle of nuclear magnetic resonance. There have been discussed the operating principle, the block diagram and operating parameters of the meter. It can be applied to measurements of induction in electromagnets of wide-line radio-spectrometers EPR and NMR and in calibration stands of magnetic induction values. Frequency range of an autodyne oscillator from 0,6 up to 86 MHz for protons is corresponding to the field range from 0.016 up to 2T. Applicaton of other nuclei, such as 7Li and 2D is also foreseen. The induction measurement is carried over automatically, and the NMR signal and value of measured induction are displayed on a monitor screen. (author)
Vamos¸, C˘alin
2013-01-01
Our book introduces a method to evaluate the accuracy of trend estimation algorithms under conditions similar to those encountered in real time series processing. This method is based on Monte Carlo experiments with artificial time series numerically generated by an original algorithm. The second part of the book contains several automatic algorithms for trend estimation and time series partitioning. The source codes of the computer programs implementing these original automatic algorithms are given in the appendix and will be freely available on the web. The book contains clear statement of the conditions and the approximations under which the algorithms work, as well as the proper interpretation of their results. We illustrate the functioning of the analyzed algorithms by processing time series from astrophysics, finance, biophysics, and paleoclimatology. The numerical experiment method extensively used in our book is already in common use in computational and statistical physics.
P.KEERTHANAA, K.JEEVITHA, V.NAVINA, G.INDIRA, S.JAYAMANI
2013-01-01
The Primary Aim Of The Project Is To Design, Develop And Implement Automatic Wall Painting Robot Which Helps To Achieve Low Cost Painting Equipment. Despite The Advances In Robotics And Its Wide Spreading Applications, Interior Wall Painting Has Shared Little In Research Activities. The Painting Chemicals Can Cause Hazards To The Human Painters Such As Eye And Respiratory System Problems. Also The Nature Of Painting Procedure That Requires Repeated Work And Hand Rising Makes It Boring, Time A...
Lígia Maria da Silva Ribeiro; Gabriel de Sousa Torcato David
2007-01-01
To profit from the data collected by the SIGARRA academic IS, a systematic setof graphs and statistics has been added to it and are available on-line. Thisanalytic information can be automatically included in a flexible yearly report foreach program as well as in a synthesis report for the whole school. Somedifficulties in the interpretation of some graphs led to the definition of new keyindicators and the development of a data warehouse across the university whereeffective data consolidation...
Automatic Inductive Programming Tutorial
Aler, Ricardo
2006-01-01
Computers that can program themselves is an old dream of Artificial Intelligence, but only nowadays there is some progress of remark. In relation to Machine Learning, a computer program is the most powerful structure that can be learned, pushing the final goal well beyond neural networks or decision trees. There are currently many separate areas, working independently, related to automatic programming, both deductive and inductive. The first goal of this tutorial is to give to the attendants ...
Mueller Loose, Simone
Consumers' food decisions are to a large extent shaped by automatic processes, which are either internally directed through learned habits and routines or externally influenced by context factors and visual information triggers. Innovative research methods such as eye tracking, choice experiments...... and food diaries allow us to better understand the impact of unconscious processes on consumers' food choices. Simone Mueller Loose will provide an overview of recent research insights into the effects of habit and context on consumers' food choices....
Automatic Differentiation Variational Inference
Kucukelbir, Alp; Tran, Dustin; Ranganath, Rajesh; Gelman, Andrew; Blei, David M.
2016-01-01
Probabilistic modeling is iterative. A scientist posits a simple model, fits it to her data, refines it according to her analysis, and repeats. However, fitting complex models to large data is a bottleneck in this process. Deriving algorithms for new models can be both mathematically and computationally challenging, which makes it difficult to efficiently cycle through the steps. To this end, we develop automatic differentiation variational inference (ADVI). Using our method, the scientist on...
Automaticity or active control
Tudoran, Ana Alina; Olsen, Svein Ottar
This study addresses the quasi-moderating role of habit strength in explaining action loyalty. A model of loyalty behaviour is proposed that extends the traditional satisfaction–intention–action loyalty network. Habit strength is conceptualised as a cognitive construct to refer to the psychologic......, respectively, between intended loyalty and action loyalty. At high levels of habit strength, consumers are more likely to free up cognitive resources and incline the balance from controlled to routine and automatic-like responses....
Automatic digital image registration
Goshtasby, A.; Jain, A. K.; Enslin, W. R.
1982-01-01
This paper introduces a general procedure for automatic registration of two images which may have translational, rotational, and scaling differences. This procedure involves (1) segmentation of the images, (2) isolation of dominant objects from the images, (3) determination of corresponding objects in the two images, and (4) estimation of transformation parameters using the center of gravities of objects as control points. An example is given which uses this technique to register two images which have translational, rotational, and scaling differences.
Automatic radioactive waste recycling
The production of a plutonium ingot by calcium reduction process at CEA/Valduc generates a residue called 'slag'. This article introduces the recycling unit which is dedicated to the treatment of slags. The aim is to separate and to recycle the plutonium trapped in this bulk on the one hand, and to generate a disposable waste from the slag on the other hand. After a general introduction of the facilities, some elements will be enlightened, particularly the dissolution step, the filtration and the drying equipment. Reflections upon technological constraints will be proposed, and the benefits of a fully automatic recycling unit of nuclear waste will also be stressed. (authors)
Automatic Configuration in NTP
Jiang Zongli(蒋宗礼); Xu Binbin
2003-01-01
NTP is nowadays the most widely used distributed network time protocol, which aims at synchronizing the clocks of computers in a network and keeping the accuracy and validation of the time information which is transmitted in the network. Without automatic configuration mechanism, the stability and flexibility of the synchronization network built upon NTP protocol are not satisfying. P2P's resource discovery mechanism is used to look for time sources in a synchronization network, and according to the network environment and node's quality, the synchronization network is constructed dynamically.
A measuring system is disclosed for surveying and very accurately positioning objects with respect to a reference line. A principal use of this surveying system is for accurately aligning the electromagnets which direct a particle beam emitted from a particle accelerator. Prior art surveying systems require highly skilled surveyors. Prior art systems include, for example, optical surveying systems which are susceptible to operator reading errors, and celestial navigation-type surveying systems, with their inherent complexities. The present invention provides an automatic readout micrometer which can very accurately measure distances. The invention has a simplicity of operation which practically eliminates the possibilities of operator optical reading error, owning to the elimination of traditional optical alignments for making measurements. The invention has an extendable arm which carries a laser surveying target. The extendable arm can be continuously positioned over its entire length of travel by either a coarse or fine adjustment without having the fine adjustment outrun the coarse adjustment until a reference laser beam is centered on the target as indicated by a digital readout. The length of the micrometer can then be accurately and automatically read by a computer and compared with a standardized set of alignment measurements. Due to its construction, the micrometer eliminates any errors due to temperature changes when the system is operated within a standard operating temperature range
Automatic personnel contamination monitor
United Nuclear Industries, Inc. (UNI) has developed an automatic personnel contamination monitor (APCM), which uniquely combines the design features of both portal and hand and shoe monitors. In addition, this prototype system also has a number of new features, including: micro computer control and readout, nineteen large area gas flow detectors, real-time background compensation, self-checking for system failures, and card reader identification and control. UNI's experience in operating the Hanford N Reactor, located in Richland, Washington, has shown the necessity of automatically monitoring plant personnel for contamination after they have passed through the procedurally controlled radiation zones. This final check ensures that each radiation zone worker has been properly checked before leaving company controlled boundaries. Investigation of the commercially available portal and hand and shoe monitors indicated that they did not have the sensitivity or sophistication required for UNI's application, therefore, a development program was initiated, resulting in the subject monitor. Field testing shows good sensitivity to personnel contamination with the majority of alarms showing contaminants on clothing, face and head areas. In general, the APCM has sensitivity comparable to portal survey instrumentation. The inherit stand-in, walk-on feature of the APCM not only makes it easy to use, but makes it difficult to bypass. (author)
Automatic MR volume registration and its evaluation for the pelvis and prostate
A three-dimensional (3D) mutual information registration method was created and used to register MRI volumes of the pelvis and prostate. It had special features to improve robustness. First, it used a multi-resolution approach and performed registration from low to high resolution. Second, it used two similarity measures, correlation coefficient at lower resolutions and mutual information at full resolution, because of their particular advantages. Third, we created a method to avoid local minima by restarting the registration with randomly perturbed parameters. The criterion for restarting was a correlation coefficient below an empirically determined threshold. Experiments determined the accuracy of registration under conditions found in potential applications in prostate cancer diagnosis, staging, treatment and interventional MRI (iMRI) guided therapies. Images were acquired in the diagnostic (supine) and treatment position (supine with legs raised). Images were also acquired as a function of bladder filling and the time interval between imaging sessions. Overall studies on three patients and three healthy volunteers, when both volumes in a pair were obtained in the diagnostic position under comparable conditions, bony landmarks and prostate 3D centroids were aligned within 1.6± 0.2mm and 1.4±0.2 mm, respectively, values only slightly larger than a voxel. Analysis suggests that actual errors are smaller because of the uncertainty in landmark localization and prostate segmentation. Between the diagnostic and treatment positions, bony landmarks continued to register well, but prostate centroids moved towards the posterior 2.8-3.4 mm. Manual cropping to remove voxels in the legs was necessary to register these images. In conclusion, automatic, rigid body registration is probably sufficiently accurate for many applications in prostate cancer. For potential iMRI-guided treatments, the small prostate displacement between the diagnostic and treatment positions can
Dussol, David; Druault, Philippe; Mallat, Bachar; Delacroix, Sylvain; Germain, Grégory
2016-07-01
When performing Particle Image Velocimetry (PIV) measurements in complex fluid flows with moving interfaces and a two-phase flow, it is necessary to develop a mask to remove non-physical measurements. This is the case when studying, for example, the complex bubble sweep-down phenomenon observed in oceanographic research vessels. Indeed, in such a configuration, the presence of an unsteady free surface, of a solid-liquid interface and of bubbles in the PIV frame, leads to generate numerous laser reflections and therefore spurious velocity vectors. In this note, an image masking process is developed to successively identify the boundaries of the ship and the free surface interface. As the presence of the solid hull surface induces laser reflections, the hull edge contours are simply detected in the first PIV frame and dynamically estimated for consecutive ones. As for the unsteady surface determination, a specific process is implemented like the following: i) the edge detection of the gradient magnitude in the PIV frame, ii) the extraction of the particles by filtering high-intensity large areas related to the bubbles and/or hull reflections, iii) the extraction of the rough region containing these particles and their reflections, iv) the removal of these reflections. The unsteady surface is finally obtained with a fifth-order polynomial interpolation. The resulted free surface is successfully validated from the Fourier analysis and by visualizing selected PIV images containing numerous spurious high intensity areas. This paper demonstrates how this data analysis process leads to PIV images database without reflections and an automatic detection of both the free surface and the rigid body. An application of this new mask is finally detailed, allowing a preliminary analysis of the hydrodynamic flow.
Automatic Speaker Recognition System
Parul,R. B. Dubey
2012-12-01
Full Text Available Spoken language is used by human to convey many types of information. Primarily, speech convey message via words. Owing to advanced speech technologies, people's interactions with remote machines, such as phone banking, internet browsing, and secured information retrieval by voice, is becoming popular today. Speaker verification and speaker identification are important for authentication and verification in security purpose. Speaker identification methods can be divided into text independent and text-dependent. Speaker recognition is the process of automatically recognizing speaker voice on the basis of individual information included in the input speech waves. It consists of comparing a speech signal from an unknown speaker to a set of stored data of known speakers. This process recognizes who has spoken by matching input signal with pre- stored samples. The work is focussed to improve the performance of the speaker verification under noisy conditions.
P.KEERTHANAA, K.JEEVITHA, V.NAVINA, G.INDIRA, S.JAYAMANI
2013-07-01
Full Text Available The Primary Aim Of The Project Is To Design, Develop And Implement Automatic Wall Painting Robot Which Helps To Achieve Low Cost Painting Equipment. Despite The Advances In Robotics And Its Wide Spreading Applications, Interior Wall Painting Has Shared Little In Research Activities. The Painting Chemicals Can Cause Hazards To The Human Painters Such As Eye And Respiratory System Problems. Also The Nature Of Painting Procedure That Requires Repeated Work And Hand Rising Makes It Boring, Time And Effort Consuming. When Construction Workers And Robots Are Properly Integrated In Building Tasks, The Whole Construction Process Can Be Better Managed And Savings In Human Labour And Timing Are Obtained As A Consequence. In Addition, It Would Offer The Opportunity To Reduce Or Eliminate Human Exposure To Difficult And Hazardous Environments, Which Would Solve Most Of The Problems Connected With Safety When Many Activities Occur At The Same Time. These Factors Motivate The Development Of An Automated Robotic Painting System.
Automatic alkaloid removal system.
Yahaya, Muhammad Rizuwan; Hj Razali, Mohd Hudzari; Abu Bakar, Che Abdullah; Ismail, Wan Ishak Wan; Muda, Wan Musa Wan; Mat, Nashriyah; Zakaria, Abd
2014-01-01
This alkaloid automated removal machine was developed at Instrumentation Laboratory, Universiti Sultan Zainal Abidin Malaysia that purposely for removing the alkaloid toxicity from Dioscorea hispida (DH) tuber. It is a poisonous plant where scientific study has shown that its tubers contain toxic alkaloid constituents, dioscorine. The tubers can only be consumed after it poisonous is removed. In this experiment, the tubers are needed to blend as powder form before inserting into machine basket. The user is need to push the START button on machine controller for switching the water pump ON by then creating turbulence wave of water in machine tank. The water will stop automatically by triggering the outlet solenoid valve. The powders of tubers are washed for 10 minutes while 1 liter of contaminated water due toxin mixture is flowing out. At this time, the controller will automatically triggered inlet solenoid valve and the new water will flow in machine tank until achieve the desire level that which determined by ultra sonic sensor. This process will repeated for 7 h and the positive result is achieved and shows it significant according to the several parameters of biological character ofpH, temperature, dissolve oxygen, turbidity, conductivity and fish survival rate or time. From that parameter, it also shows the positive result which is near or same with control water and assuming was made that the toxin is fully removed when the pH of DH powder is near with control water. For control water, the pH is about 5.3 while water from this experiment process is 6.0 and before run the machine the pH of contaminated water is about 3.8 which are too acid. This automated machine can save time for removing toxicity from DH compared with a traditional method while less observation of the user. PMID:24783795
Making automatic differentiation truly automatic : coupling PETSc with ADIC
Despite its name, automatic differentiation (AD) is often far from an automatic process. often one must specify independent and dependent variables, indicate the derivative quantities to be computed, and perhaps even provide information about the structure of the Jacobians or Hessians being computed. However, when AD is used in conjunction with a toolkit with well-defined interfaces, many of these issues do not arise. They describe recent research into coupling the ADIC automatic differentiation tool with PETSc, a toolkit for the parallel numerical solution of PDEs. This research leverages the interfaces and objects of PETSc to make the AD process very nearly transparent
Automatic Kurdish Dialects Identification
Hossein Hassani
2016-02-01
Full Text Available Automatic dialect identification is a necessary Lan guage Technology for processing multi- dialect languages in which the dialects are linguis tically far from each other. Particularly, this becomes crucial where the dialects are mutually uni ntelligible. Therefore, to perform computational activities on these languages, the sy stem needs to identify the dialect that is the subject of the process. Kurdish language encompasse s various dialects. It is written using several different scripts. The language lacks of a standard orthography. This situation makes the Kurdish dialectal identification more interesti ng and required, both form the research and from the application perspectives. In this research , we have applied a classification method, based on supervised machine learning, to identify t he dialects of the Kurdish texts. The research has focused on two widely spoken and most dominant Kurdish dialects, namely, Kurmanji and Sorani. The approach could be applied to the other Kurdish dialects as well. The method is also applicable to the languages which are similar to Ku rdish in their dialectal diversity and differences.
Electronic amplifiers for automatic compensators
Polonnikov, D Ye
1965-01-01
Electronic Amplifiers for Automatic Compensators presents the design and operation of electronic amplifiers for use in automatic control and measuring systems. This book is composed of eight chapters that consider the problems of constructing input and output circuits of amplifiers, suppression of interference and ensuring high sensitivity.This work begins with a survey of the operating principles of electronic amplifiers in automatic compensator systems. The succeeding chapters deal with circuit selection and the calculation and determination of the principal characteristics of amplifiers, as
Clothes Dryer Automatic Termination Evaluation
TeGrotenhuis, Ward E.
2014-10-01
Volume 2: Improved Sensor and Control Designs Many residential clothes dryers on the market today provide automatic cycles that are intended to stop when the clothes are dry, as determined by the final remaining moisture content (RMC). However, testing of automatic termination cycles has shown that many dryers are susceptible to over-drying of loads, leading to excess energy consumption. In particular, tests performed using the DOE Test Procedure in Appendix D2 of 10 CFR 430 subpart B have shown that as much as 62% of the energy used in a cycle may be from over-drying. Volume 1 of this report shows an average of 20% excess energy from over-drying when running automatic cycles with various load compositions and dryer settings. Consequently, improving automatic termination sensors and algorithms has the potential for substantial energy savings in the U.S.
Prospects for de-automatization.
Kihlstrom, John F
2011-06-01
Research by Raz and his associates has repeatedly found that suggestions for hypnotic agnosia, administered to highly hypnotizable subjects, reduce or even eliminate Stroop interference. The present paper sought unsuccessfully to extend these findings to negative priming in the Stroop task. Nevertheless, the reduction of Stroop interference has broad theoretical implications, both for our understanding of automaticity and for the prospect of de-automatizing cognition in meditation and other altered states of consciousness. PMID:20356765