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

In this paper the problem of simulation of constrained mechanical systems is addressed. In modeling multi-body mechanical systems, the Lagrange formulation produces a redundant set of differential-algebraic equations, the integration 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.