Approximation and existence in vibro-impact

We consider a dynamical system with a finite number of degrees of freedom, in generalized coordinates, subject to unilateral constraints, which nl-e s mooth, but not necessarily convex. When the constraints are saturated, we d efine an impact law involving a restitution coefficient e is an element of [0,1]. We introduce a numerical scheme and we prove the convergence of a su bsequence of approximate solutions to a solution of Cauchy's problem; this gives the existence solutions as a by-product of our analysis. (C) 1999 Aca demie des sciences/Editions scientifiques et medicales Elsevier SAS.