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

Laetitia Paoli

Mathematics and Computers in Simulation (MATCOM), 2015, vol. 118, issue C, 302-309

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.

Keywords: Discrete mechanical system; Time-dependent constraints; Differential inclusion; Inelastic shocks; Time-stepping scheme (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:118:y:2015:i:c:p:302-309

DOI: 10.1016/j.matcom.2014.11.015

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