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 that is 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 Laplace transform technique. Finally, a slider crank mechanism with eccentricity is considered as an example of application in order to illustrated how the violation of constraints can be affected by different factors such as the Baumgarte parameters, integrator, time step and initial guesses.
- Design Engineering Division and Computers in Engineering Division
A Parametric Study on the Baumgarte Stabilization Method for Forward Dynamics of Constrained Multibody Systems
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Flores, P, Machado, M, Seabra, E, & Tavares da Silva, M. "A Parametric Study on the Baumgarte Stabilization Method for Forward Dynamics of Constrained Multibody Systems." Proceedings of the ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 4: 7th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B and C. San Diego, California, USA. August 30–September 2, 2009. pp. 73-82. ASME. https://doi.org/10.1115/DETC2009-86362
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