Methods for constraint violation suppression in the numerical simulation of constrained multibody systems – A comparative study

Multibody systems are frequently modeled as constrained systems, and the arising governing equations incorporate the closing constraint equations at the acceleration level. One consequence of accumulation of integration truncation errors is the phenomenon of violation of the lower-order constraint equations by the numerical solutions to the governing equations. The constraint drift usually tends to increase in time and may spoil reliability of the simulation results. In this paper a comparative study of three methods for constraint violation suppression is presented: the popular Baumgarte’s constraint violation stabilization method, a projective scheme for constraint violation elimination, and a novel scheme patterned after that proposed recently by Braun and Goldfarb [D.J. Braun, M. Goldfarb, Eliminating constraint drift in the numerical simulation of constrained dynamical systems, Comput. Meth. Appl. Mech. Engrg., 198 (2009) 3151–3160]. The methods are confronted with respect to simplicity in applications, numerical effectiveness and influence on accuracy of the constraint-consistent motion.