A catching-up algorithm for multibody dynamics with impacts and dry friction

In the beginning of the 80s, a rigorous mathematical framework was developed for the dynamics of multibody systems with perfect unilateral contacts, particularly due to the contributions of Schatzman and Moreau. Efficient numerical methods have been proposed, for instance Moreau's NonSmooth Contact Dynamics (NSCD) (Moreau, 1999), which was then extended by Jean to cases with friction (Jean, 1999). But the algorithm, in the latter case, is no longer the time discretization of an evolution problem. In this work, we derive a new algorithm from the time discretization of an evolution problem for multibody dynamics with contacts and friction. Our algorithm has many points in common with the one of Jean and Moreau, but it converges reliably and fixes some energetic inconsistencies. The similarities and differences between the algorithms are illustrated on three planar archetypal examples.