AN EXISTENCE RESULT FOR VIBRATIONS WITH UNILATERAL CONSTRAINTS

We are motivated by the study of dynamical systems with a finite number of degrees of freedom, subject to unilateral convex constraints without loss of energy at impacts. If we denote the set of constraints by K, the motion is described by , where ψK is the indicatrix function of K. More generally we consider dynamical systems with a convex potential described by , where φ is a proper, convex, lower semicontinuous function. We prove that these systems possess a solution whose kinetic energy is conserved through impact in the first case, or more generally, whose energy is a continuous function of time in the second case.