An existence result for non-smooth vibro-impact problems

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:211

Article

Paoli, L

关键词: vibro-impact;    non-smooth convex constraints;    measure differential inclusion;    inelastic shocks;    time-discretization scheme;    convergence;    existence;   

DOI  :  10.1016/j.jde.2004.11.008

来源: Elsevier

【 摘 要 】

We are interested in mechanical systems with a finite number of degrees of freedom submitted to frictionless unilateral constraints. We consider the case of a convex, non-smooth set of admissible positions given by K = {q epsilon R-d; phi(alpha) (q) > 0, 1 <= alpha <= v}, v >= 1, and we assume inelastic shocks at impacts. We propose a time-discretization of the measure differential inclusion which describes the dynamics and we prove the convergence of the approximate solutions to a limit motion which satisfies the constraints. Moreover, if the geometric properties ensuring continuity on data hold at the limit, we show that the transmission of velocities at impacts follows the inelastic shocks rule. (c) 2004 Elsevier Inc. All rights reserved.

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