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Journal Articles Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik Year : 2011

A formulation of the linear discrete Coulomb friction problem via convex optimization

Abstract

This paper presents a new formulation of the dynamical Coulomb friction problem in finite dimension with discretized time. The novelty of our approach is to capture and treat directly the friction model as a parametric quadratic optimization problem with second-order cone constraints coupled with a fixed point equation. This intrinsic formulation allows a simple existence proof under reasonable assumptions, as well as a variety of solution algorithms. We study mechanical interpretations of these assumptions, showing in particular that they are actually necessary and sufficient for a basic example similar to the so-called ''paradox of Painlevé''. Finally, we present some implementations and experiments to illustrate the practical aspect of our work.
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Dates and versions

inria-00495734 , version 1 (28-06-2010)

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Cite

Vincent Acary, Florent Cadoux, Claude Lemaréchal, Jérôme Malick. A formulation of the linear discrete Coulomb friction problem via convex optimization. Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2011, 91 (2), pp.155-175. ⟨10.1002/zamm.201000073⟩. ⟨inria-00495734⟩
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