Integration through singularities

Abstract

The numerical integration of the equations of motion of a multi-body system in index-1-formulation (differential-algebraic equations) sometimes breaks down, because there is a singularity on the manifold of consistent positions. This can be the case even if there is a continuously differentiable solution of the equations. In this article it is shown how to get through such singularities in very common situations by "blowing up" the position constraint equations. A very simple proof for the finiteness of the algorithm is given and explained with simple, but non-trivial examples. © 2003 WILEY-VCH Verlag GmbH & Co. KGaA.