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

Vincent Acary 1 Florent Cadoux 1 Claude Lemaréchal 1 Jérôme Malick 1
1 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
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.
Complete list of metadatas

Cited literature [29 references]  Display  Hide  Download

https://hal.inria.fr/inria-00495734
Contributor : Vincent Acary <>
Submitted on : Monday, June 28, 2010 - 4:24:57 PM
Last modification on : Friday, February 22, 2019 - 11:44:20 AM
Long-term archiving on : Thursday, June 30, 2011 - 1:06:48 PM

File

ptfixe.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

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, Wiley-VCH Verlag, 2011, 91 (2), pp.155-175. ⟨10.1002/zamm.201000073⟩. ⟨inria-00495734⟩

Share

Metrics

Record views

805

Files downloads

1119