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.
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e-mail: pflores@dem.uminho.pt
e-mail: margarida@dem.uminho.pt
e-mail: eseabra@dem.uminho.pt
e-mail: miguelsilva@ist.utl.pt
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January 2011
Research Papers
A Parametric Study on the Baumgarte Stabilization Method for Forward Dynamics of Constrained Multibody Systems
Paulo Flores,
Paulo Flores
Departamento de Engenharia Mecânica,
e-mail: pflores@dem.uminho.pt
Universidade do Minho, Campus de Azurém
, 4800-058 Guimarães, Portugal
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Margarida Machado,
Margarida Machado
Departamento de Engenharia Mecânica,
e-mail: margarida@dem.uminho.pt
Universidade do Minho, Campus de Azurém
, 4800-058 Guimarães, Portugal
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Eurico Seabra,
Eurico Seabra
Departamento de Engenharia Mecânica,
e-mail: eseabra@dem.uminho.pt
Universidade do Minho, Campus de Azurém
, 4800-058 Guimarães, Portugal
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Miguel Tavares da Silva
Miguel Tavares da Silva
Instituto de Engenharia Mecânica (IDMEC),
e-mail: miguelsilva@ist.utl.pt
Instituto Superior Técnico
, Avenida Rovisco Pais 1, 1049-001 Lisboa, Portugal
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Paulo Flores
Departamento de Engenharia Mecânica,
Universidade do Minho, Campus de Azurém
, 4800-058 Guimarães, Portugale-mail: pflores@dem.uminho.pt
Margarida Machado
Departamento de Engenharia Mecânica,
Universidade do Minho, Campus de Azurém
, 4800-058 Guimarães, Portugale-mail: margarida@dem.uminho.pt
Eurico Seabra
Departamento de Engenharia Mecânica,
Universidade do Minho, Campus de Azurém
, 4800-058 Guimarães, Portugale-mail: eseabra@dem.uminho.pt
Miguel Tavares da Silva
Instituto de Engenharia Mecânica (IDMEC),
Instituto Superior Técnico
, Avenida Rovisco Pais 1, 1049-001 Lisboa, Portugale-mail: miguelsilva@ist.utl.pt
J. Comput. Nonlinear Dynam. Jan 2011, 6(1): 011019 (9 pages)
Published Online: October 13, 2010
Article history
Received:
July 30, 2009
Revised:
December 10, 2009
Online:
October 13, 2010
Published:
October 13, 2010
Citation
Flores, P., Machado, M., Seabra, E., and Tavares da Silva, M. (October 13, 2010). "A Parametric Study on the Baumgarte Stabilization Method for Forward Dynamics of Constrained Multibody Systems." ASME. J. Comput. Nonlinear Dynam. January 2011; 6(1): 011019. https://doi.org/10.1115/1.4002338
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