CONTINUOUS DEPENDENCE ON DATA FOR VIBRO-IMPACT PROBLEMS

We consider vibro-impact problems, i.e. mechanical systems with a finite number of degrees of freedom subject to frictionless unilateral constraints. The dynamics is described by a second-order measure differential inclusion completed by an impact law of Newton's type. Motivated by the computation of approximate solutions, we study in this paper the continuous dependence of solutions on data. When several constraints can be active at the same time, continuity on data does not hold in general and an example of such a behavior is presented. We then propose a criterion involving the geometry of the active constraints along the limit trajectory which ensures continuity on data.

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