Constraint Gradient Projective Method for Stabilized Dynamic Simulation of Constrained Multibody Systems

Abstract

Constraint gradient projective method for stabilization of constraint violation during integration of constrained multibody systems is in the focus of the paper. Different mathematical models for constrained MBS dynamic simulation on manifolds are surveyed and violation of kinematical constraints is discussed. As an extension of the previous work focused on the integration procedures of the holonomic systems, the constraint gradient projective method for generally constrained mechanical systems is discussed. By adopting differentialgeometric point of view, the geometric and stabilization issues of the method are addressed. It is shown that the method can be applied for stabilization of holonomic and non-holonomic constraints in Pfaffian and general form.

Constraint Stabilization of Mechanical Systems in Ordinary Differential Equations Form

“…Terze et al propose to select n − c independent coordinates from x, based on a weighting related to M (interpreted as a metric tensor of the configuration space, according to reference [47]), and preserve them, while eliminating drift with respect to the remaining co-ordinates [48][49][50].…”