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Journal of Convex Analysis 23 (2016), No. 3, 849--876
Copyright Heldermann Verlag 2016

Multibody Dynamics with Unilateral Constraints and Dry Friction: How the Contact Dynamics Approach May Handle Coulomb's Law Indeterminacies?

Laetitia Paoli
Institut Camille Jordan, Université de Lyon, 23 Rue du Docteur Paul Michelon, 42023 St. Etienne Cedex 2, France

For the numerical simulation of mechanical systems subjected to unilateral constraints, the Contact Dynamics approach has been developped by J. J. Moreau since the mid 80's. The core idea consists in applying a discrete contact law S to the left "free" velocity computed at each time-step. The mapping S should of course mimic the behavior of the system in case of contact. But, when dry friction occurs, the dynamics may exhibit indeterminacies of Painlevé's paradoxes type. Then a natural question arises: how a deterministic discrete contact law may handle such phenomena? An answer has been given through numerical experiments by J. J. Moreau and is subtanciated in this paper by introducing the notions of asymptotic consistency of the discrete contact law with respect to Coulomb's friction and asymptotic indeterminacy of the scheme.

Keywords: Multibody dynamics, unilateral constraints, Coulomb's friction, time-stepping scheme, asymptotic consistency, indeterminacy

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