A Time-Stepping Scheme for Multibody Dynamics with Unilateral Constraints

We are interested in frictionless vibro-impact problems i.e. systems of rigid bodies submitted to perfect unilateral constraints. The dynamics is described by a second order measure differential inclusion for the unknown positions, completed by a constitutive impact law of Newton's type. Motivated by the computation of approximate solutions, we propose a time-stepping scheme deriving from an Euler discretization of the measure differential inclusion. Convergence results in the single constraint case are recalled and extended to the multi-contraint case.