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Time-Stepping Approximation of Rigid-Body Dynamics with Perfect Unilateral Constraints. I: The Inelastic Impact Case

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Abstract

We consider a discrete mechanical system with a non-trivial mass matrix, subjected to perfect unilateral constraints described by the geometrical inequalities \({f_{\alpha} (q) \geqq 0, \alpha \in \{1, \dots, \nu\} (\nu \geqq 1)}\). We assume that the transmission of the velocities at impact is governed by Newton’s Law with a coefficient of restitution e = 0 (so that the impact is inelastic). We propose a time-discretization of the second order differential inclusion describing the dynamics, which generalizes the scheme proposed in Paoli (J Differ Equ 211:247–281, 2005) and, for any admissible data, we prove the convergence of approximate motions to a solution of the initial-value problem.

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  1. LaMUSE (Laboratoire de Mathématiques del’Université de Saint-Etienne), University of Lyon, University of Saint-Etienne, Jean Monnet, 23 rue du Docteur Paul Michelon, 42023, Saint-Etienne Cedex 2, France

    L. Paoli

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  1. L. Paoli
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Correspondence to L. Paoli.

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Communicated by S. Antman

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Paoli, L. Time-Stepping Approximation of Rigid-Body Dynamics with Perfect Unilateral Constraints. I: The Inelastic Impact Case. Arch Rational Mech Anal 198, 457–503 (2010). https://doi.org/10.1007/s00205-010-0311-0

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  • DOI: https://doi.org/10.1007/s00205-010-0311-0

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