A globally stable convergent algorithm for the integration of constrained mechanical systems

Abstract

In this paper the problem of simulation of con- strained mechanical systems is addressed. In modeling multi- body mechanical systems, the Lagrange formulation produces a redundant set of differential-algebraic equations, the integra- tion of which can lead to several difficulties, for example the drift of the “constraint violation”. One of the most popular approaches to alleviate this issue is the so-called Baumgarte’s method that relies on a linear feedback mechanism. This method can however lead to numerical instabilities when applied to nonlinear (mechanical) systems. The objective of this study is to propose a new method that ensures existence of solutions and makes the constraint manifold asymptotically attractive. The proposed technique is illustrated by means of a simple example.