On the optimal scaling of index three DAEs in multibody dynamics

We propose a preconditioning strategy for the governing equations of multibody systems in index-3 differential-algebraic form. The method eliminates the amplification of errors and the ill-conditioning which affect numerical solutions of high index differential algebraic equations for small time steps. We develop a new theoretical analysis of the perturbation problem and we apply it to the derivation of preconditioners for the Newmark family of integration schemes. The theoretical results are confirmed by numerical experiments.