A unified variational model for the dynamics of perfect unilateral constraints

We consider a mechanical system with a finite number of degrees of freedom submitted to given perfect unilateral constraints f alpha less than or equal to 0, alpha = 1,..., nu. Following Moreau's approach, we present a synthetic model described by a single differential inclusion, the problem P, which governs the evolution of the system in the presence of shocks with the arbitrary restitution coefficient e, 0 less than or equal to e less than or equal to 1. We show first that the possible (generalized) solutions still possess the same general properties as in the inelastic case, and in the case of a single constraint f(q) less than or equal to 0, we prove the existence of a (essentially non-unique) generalized solution under the condition that f is of class C-1,C-beta, beta > 1/2. (C) Elsevier, Paris.