The dynamic equations of motion of the constrained multibody mechanical system are mixed differential-algebraic equations (DAE). The DAE systems cannot be solved using numerical integration methods that are commonly used for solving ordinary differential equations. To solve this problem, Baumgarte proposed a constraint stabilization method in which a position and velocity terms were added in the second derivative of the constraint equation. The disadvantage of this method is that there is no reliable method for selecting the coefficients of the position and velocity terms. Improper selection of these coefficients can lead to erroneous results. In this study, stability analysis methods in digital control theory are used to solve this problem. Correct choice of the coefficients for the Runge-Kutta method is found.
Stabilization of Baumgarte’s Method Using the Runge-Kutta Approach
Contributed by the Design Automation Committee for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received April 2000; revised March 2002. Associate Editor: H. Lankarani.
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Lin, S., and Huang, J. (November 26, 2002). "Stabilization of Baumgarte’s Method Using the Runge-Kutta Approach ." ASME. J. Mech. Des. December 2002; 124(4): 633–641. https://doi.org/10.1115/1.1519277
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