A sweeping process approach to inelastic contact problems with general inertia operators

The dynamics of systems with a finite number of degrees of freedom and nontrivial inertia matrix which are submitted to a single perfect purely inelastic unilateral constraint is studied. By adopting the measure differential formulation of J.J. Moreau, a velocity-based time-stepping method is developed, reminiscent of the catching-up algorithm for sweeping processes. It is shown that the numerical solutions converge to a solution of the problem, under a weaker assumption on the constraint as compared to position-based methods.