Penalty Approximation for Non-smooth Constraints in Vibroimpact

We examine the penalty approximation of the free motion of a material point in an angular domain; we choose an over-damped penalty approximation, and we prove that if the first impact point is not at the vertex, then the limit of the approximation exists and is described by Moreauʹs rule for inelastic impacts. The proofs rely on validated asymptotics and use some classical tools of the theory of dynamical systems.