A Parametric Study on the Baumgarte Stabilization Method for Forward Dynamics of Constrained Multibody Systems
- 13 October 2010
- journal article
- Published by ASME International in Journal of Computational and Nonlinear Dynamics
- Vol. 6 (1), 011019
- https://doi.org/10.1115/1.4002338
Abstract
This paper presents and discusses the results obtained from a parametric study on the Baumgarte stabilization method for forward dynamics of constrained multibody systems. The main purpose of this work is to analyze the influence of the variables that affect the violation of constraints, chiefly the values of the Baumgarte parameters, the integration method, the time step, and the quality of the initial conditions for the positions. In the sequel of this process, the formulation of the rigid multibody systems is reviewed. The generalized Cartesian coordinates are selected as the variables to describe the bodies’ degrees of freedom. The formulation of the equations of motion uses the Newton–Euler approach, augmented with the constraint equations that lead to a set of differential algebraic equations. Furthermore, the main issues related to the stabilization of the violation of constraints based on the Baumgarte approach are revised. Special attention is also given to some techniques that help in the selection process of the values of the Baumgarte parameters, namely, those based on the Taylor’s series and the Laplace transform technique. Finally, a slider-crank mechanism with eccentricity is considered as an example of application in order to illustrate how the violation of constraints can be affected by different factors.Keywords
This publication has 25 references indexed in Scilit:
- A self-stabilized algorithm for enforcing constraints in multibody systemsInternational Journal of Solids and Structures, 2003
- Stabilization Method for Numerical Integration of Multibody Mechanical SystemsJournal of Mechanical Design, 1998
- Investigation of a New Formulation of the Lagrange Method for Constrained Dynamic SystemsJournal of Applied Mechanics, 1997
- Augmented lagrangian and mass-orthogonal projection methods for constrained multibody dynamicsNonlinear Dynamics, 1996
- An orthonormal tangent space method for constrained multibody systemsComputer Methods in Applied Mechanics and Engineering, 1995
- Geometric Elimination of Constraint Violations in Numerical Simulation of Lagrangian EquationsJournal of Mechanical Design, 1994
- Stabilization of computational procedures for constrained dynamical systemsJournal of Guidance, Control, and Dynamics, 1988
- Automatic integration of Euler-Lagrange equations with constraintsJournal of Computational and Applied Mathematics, 1985
- Generalized Coordinate Partitioning for Dimension Reduction in Analysis of Constrained Dynamic SystemsJournal of Mechanical Design, 1982
- Stabilization of constraints and integrals of motion in dynamical systemsComputer Methods in Applied Mechanics and Engineering, 1972