A non-damped stabilization algorithm for multibody dynamics

Abstract

The stability of integrators dealing with high order Differential Algebraic Equations (DAEs) is a major issue. The usual procedures give rise to instabilities that are not predicted by the usual linear analysis, rendering the common checks (developed for ODEs) unusable. The appearance of these difficult-to-explain and unexpected problems leads to methods that arise heavy numerical damping for avoiding them. This has the undesired consequences of lack of convergence of the methods, along with a need of smaller stepsizes. In this paper a new approach is presented. The algorithm presented here allows us to avoid the interference of the constraints in the integration, thus allowing the linear criteria to be applied. In order to do so, the integrator is applied to a set of instantaneous minimal coordinates that are obtained through the application of the null space. The new approach can be utilized along with any integration method. Some experiments using the Newmark method have been carried out, which validate the methodology and also show that the method behaves in a predictable way if one considers linear stability criteria.