Elimination of Constraint Violation and Accuracy Aspects in Numerical Simulation of Multibody Systems

Abstract

Multibody systems are often modeled as constrained systems, and theconstraint equations are involved in the dynamics formulations. To makethe arising governing equations more tractable, the constraint equationsare differentiated with respect to time, and this results in unstablenumerical solutions which may violate the lower-order constraintequations. In this paper we develop a methodology for numerically exactelimination of the constraint violations, based on appropriatecorrections of the state variables (after each integration step) withoutany modification in the motion equations. While the elimination ofviolation of position constraints may require few iterations, theviolation of velocity constraints is removed in one step. The totalenergy of the system is sometimes treated as another measure of theintegration process inaccuracy. An improved scheme for one-stepelimination of the energy constraint violation is proposed as well. Theconclusion of this paper is, however, that the energy conservation is ofminor importance as concerns the improvement of accuracy of numericalsimulations. Some test calculations are reported.