Elimination of constraint violation and accuracy aspects in numerical simulation of multibody systems

Multibody systems are often modeled as constrained systems, and the constraint equations are involved in the dynamics formulations. To make the arising governing equations more tractable, the constraint equations are differentiated with respect to time, and this results in unstable numerical solutions which may violate the lower-order constraint equations. In this paper we develop a methodology for numerically exact elimination of the constraint violations, based on appropriate corrections of the state variables (after each integration step) without any modification in the motion equations. While the elimination of violation of position constraints may require few iterations, the violation of velocity constraints is removed in one step. The total energy of the system is sometimes treated as another measure of the integration process inaccuracy. An improved scheme for one-step elimination of the energy constraint violation is proposed as well. The conclusion of this paper is, however, that the energy conservation is of minor importance as concerns the improvement of accuracy of numerical simulations. Some test calculations are reported.