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Existence and approximation for vibro-impact problems with a time-dependent set of constraints

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  • Paoli, Laetitia

Abstract

We consider a discrete mechanical system subjected to perfect time-dependent unilateral constraints, which dynamics is described by a second order measure differential inclusion. The transmission of the velocity at impacts is given by a minimization property of the kinetic energy with respect to the set of kinematically admissible post-impact velocities. We construct a sequence of feasible approximate positions by using a time-stepping algorithm inspired by a kind of Euler discretization of the differential inclusion. We prove the convergence of the approximate trajectories to a solution of the Cauchy problem and we obtain as a by-product a global existence result.

Suggested Citation

  • Paoli, Laetitia, 2015. "Existence and approximation for vibro-impact problems with a time-dependent set of constraints," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 118(C), pages 302-309.
    • Handle: RePEc:eee:matcom:v:118:y:2015:i:c:p:302-309
    DOI: 10.1016/j.matcom.2014.11.015
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