Stabilization of constraints and integrals of motion in dynamical systems
01 Jun 1972-Computer Methods in Applied Mechanics and Engineering (North-Holland)-Vol. 1, Iss: 1, pp 1-16
TL;DR: In this article, it is shown how the analytical relations can be satisfied in a stabilized manner in order to improve the numerical accuracy of the solution of the differential equations, which leads to a modified differential system which is often stable in the sense of Ljapunov.
About: This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 1972-06-01. It has received 1429 citations till now. The article focuses on the topics: Numerical partial differential equations & Delay differential equation.
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01 Jan 1989TL;DR: In this article, the authors propose a floating frame of reference formulation for large deformation problems in linear algebra, based on reference kinematics and finite element formulation for deformable bodies.
Abstract: 1. Introduction 2. Reference kinematics 3. Analytical techniques 4. Mechanics of deformable bodies 5. Floating frame of reference formulation 6. Finite element formulation 7. Large deformation problem Appendix: Linear algebra References Index.
2,125 citations
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26 Nov 2007
TL;DR: Rigid Body Dynamics Algorithms presents the subject of computational rigid-body dynamics through the medium of spatial 6D vector notation to facilitate the implementation of dynamics algorithms on a computer: shorter, simpler code that is easier to write, understand and debug, with no loss of efficiency.
Abstract: Rigid Body Dynamics Algorithms presents the subject of computational rigid-body dynamics through the medium of spatial 6D vector notation. It explains how to model a rigid-body system and how to analyze it, and it presents the most comprehensive collection of the best rigid-bodydynamics algorithms to be found in a single source. The use of spatial vector notation greatly reduces the volume of algebra which allows systems to be described using fewer equations and fewer quantities. It also allows problems to be solved in fewer steps, and solutions to be expressed more succinctly. In addition algorithms are explained simply and clearly, and are expressed in a compact form. The use of spatial vector notation facilitates the implementation of dynamics algorithms on a computer: shorter, simpler code that is easier to write, understand and debug, with no loss of efficiency.
1,057 citations
Cites methods from "Stabilization of constraints and in..."
...This method is due to Baumgarte, and is sometimes called Baumgarte stabilization (Baumgarte, 1972)....
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15 Sep 1995
TL;DR: Algorithm for the animation of male and female models performing three dynamic athletic behaviors: running, bicycling, and vaulting using control algorithms that cause a physically realistic model to perform the desired maneuver.
Abstract: This paper describes algorithms for the animation of male and female models performing three dynamic athletic behaviors: running, bicycling, and vaulting. We animate these behaviors using control algorithms that cause a physically realistic model to perform the desired maneuver. For example, control algorithms allow the simulated humans to maintain balance while moving their arms, to run or bicycle at a variety of speeds, and to perform two vaults. For each simulation, we compare the computed motion to that of humans performing similar maneuvers. We perform the comparison both qualitatively through real and simulated video images and quantitatively through simulated and biomechanical data.
696 citations
TL;DR: Quantitative comparisons between model and experiment indicate that the model reproduces the kinematic, kinetic, and muscle-coordination patterns evident when humans jump to their maximum achievable heights.
Abstract: A three-dimensional model of the human body is used to simulate a maximal vertical jump. The body is modeled as a 10-segment, 23 degree-of-freedom (dof), mechanical linkage, actuated by 54 muscles. Six generalized coordinates describe the position and orientation of the pelvis relative to the ground; the remaining nine segments branch in an open chain from the pelvis. The head, arms, and torso (HAT) are modeled as a single rigid body. The HAT articulates with the pelvis via a 3 dof ball-and-socket joint. Each hip is modeled as a 3 dof ball-and-socket joint, and each knee is modeled as a 1 dof hinge joint. Each foot is represented by a hindfoot and toes segment. The hindfoot articulates with the shank via a 2 dof universal joint, and the toes articulate with the hindfoot via a 1 dof hinge joint. Interaction of the feet with the ground is modeled using a series of spring-damper units placed under the sole of each foot. The path of each muscle is represented by either a series of straight lines or a combination of straight lines and space curves. Each actuator is modeled as a three-element, Hill-type muscle in series with tendon. A first-order process is assumed to model muscle excitation-contraction dynamics. Dynamic optimization theory is used to calculate the pattern of muscle excitations that produces a maximal vertical jump. Quantitative comparisons between model and experiment indicate that the model reproduces the kinematic, kinetic, and muscle-coordination patterns evident when humans jump to their maximum achievable heights.
572 citations
TL;DR: There is a strong interest on multibody systems in analytical and numerical mathematics resulting in reduction methods for rigorous treatment of simple models and special integration codes for ODE and DAE representations supporting the numerical efficiency.
Abstract: The paper reviews the roots, the state-of-the-art and perspectives of multibody system dynamics. Some historical remarks show that multibody system dynamics is based on classical mechanics and its engineering applications ranging from mechanisms, gyroscopes, satellites and robots to biomechanics. The state-of-the-art in rigid multibody systems is presented with reference to textbooks and proceedings. Multibody system dynamics is characterized by algorithms or formalisms, respectively, ready for computer implementation. As a result simulation and animation are most important. The state-of-the-art in flexible multibody systems is considered in a companion review by Shabana.
483 citations
Cites background from "Stabilization of constraints and in..."
...An early approach to overcome the instability is the Baumgarte stabilization [15]....
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TL;DR: In this article, a stabilization of the classical equations of two-body motion is offered, characterized by the use of the regularizing independent variable (eccentric anomaly) and by the addition of a control-term to the differential equations.
Abstract: A stabilization of the classical equations of two-body motion is offered. It is characterized by the use of the regularizing independent variable (eccentric anomaly) and by the addition of a control-term to the differential equations. This method is related to the KS-theory (Stiefel, 1970) which performed for the first time a stabilization of the Kepler motion. But in contrast to the KS-theory our method does not transform the coordinates of the particle. As far as the theory of stability and the numerical experiments are concerned we restrict ourselves to thepure Kepler motion. But, of course, the stabilizing devices will also improve the accuracy of the computation of perturbed orbits. We list, therefore, also the equations of the perturbed motion.
81 citations