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A formulation of the linear discrete Coulomb friction problem via convex optimization
Author(s) -
Acary V.,
Cadoux F.,
Lemaréchal C.,
Malick J.
Publication year - 2011
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201000073
Subject(s) - conic optimization , discretization , coulomb friction , dimension (graph theory) , mathematics , simple (philosophy) , dynamical systems theory , coulomb , parametric statistics , coulomb's law , optimization problem , quadratic equation , regular polygon , mathematical optimization , convex optimization , variety (cybernetics) , convex analysis , mathematical analysis , nonlinear system , physics , pure mathematics , geometry , philosophy , statistics , epistemology , quantum mechanics , electron
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.