Discretization schemes for constraint stabilization in nonlinear differential-algebraic systems

In this paper the problem of simulation of differential-algebraic systems is addressed. In modelling mechanical systems the use of redundant coordinates and constraints results in differential-algebraic equations, the integration of which can lead to numerical instabilities, such as the so-called drift phenomenon. In [1] the authors have proposed a globally convergent conceptual continuous-time algorithm for the integration of constrained mechanical systems which ensures the existence of solutions and global attractivity of the solution manifold. The objective of this paper is to study the numerical implementation of the algorithm presented in [1]. In addition, the stability properties of the constrained system in the manifold are studied in both the continuous and discrete time cases. The proposed technique is illustrated by means of a simple example.