A UNIFIED VARIATIONAL MODEL FOR THE DYNAMICS OF PERFECT UNILATERAL CONSTRAINTS

We consider a mechanical system with a finite number of degrees of fre edom submitted to given perfect unilateral constraints f alpha less th an or equal to 0, alpha = 1,..., nu. Following Moreau's approach, we p resent a synthetic model described by a single differential inclusion, the problem P, which governs the evolution of the system in the prese nce of shocks with the arbitrary restitution coefficient e, 0 less tha n or equal to e less than or equal to 1. We show first that the possib le (generalized) solutions still possess the same general properties a s in the inelastic case, and in the case of a single constraint f(q) l ess than or equal to 0, we prove the existence of a (essentially non-u nique) generalized solution under the condition that f is of class C-1 ,C-beta, beta > 1/2. (C) Elsevier, Paris.