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Time-Stepping Approximation of Rigid-Body Dynamics with Perfect Unilateral Constraints. II: The Partially Elastic Impact Case

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Abstract

As in Paoli (Arch Rational Mech Anal, 2010), we consider a discrete mechanical system with a non-trivial mass matrix subjected to perfect unilateral constraints described by geometrical inequalities \({f_{\alpha}(q) \geqq 0, \alpha \in \{1, \ldots, \nu \}\, (\nu \geqq 1)}\), but we assume now that the transmission of the velocities at impacts is governed by Newton’s Law with a coefficient of restitution \({e \in (0, 1]}\) (so that the impact is partially elastic). We generalize the time-discretization of the second order differential inclusion describing the dynamics proposed in Paoli (Arch Rational Mech Anal, 2010) to this case and, once again, we prove its convergence.

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  1. LaMUSE (Laboratoire de Mathématiques de l’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. II: The Partially Elastic Impact Case. Arch Rational Mech Anal 198, 505–568 (2010). https://doi.org/10.1007/s00205-010-0312-z

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  • DOI: https://doi.org/10.1007/s00205-010-0312-z

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