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New Results on Painlevé Paradoxes

Frank Génot 1 Bernard Brogliato
1 BIP - Biped Robot
Inria Grenoble - Rhône-Alpes
Abstract : In this note, we deal with dynamics of mechanical system subject to unilateral constraints. In particular, we focus on the integration of such a system that is known to be closely related to so-called Linear Complementarity Problem (LCP). Except in very simple case like codimension 1, frictionless contraints, the problem of well-posedness (existence and uniqueness of solution) to such hybrid dynamic systems (smooth dynamics + LCP + shock dynamics) is a big challenge. We concentrate on the well-known Painlevé example [Painlevé 1895], whose dynamics in a sliding regime may be singular depending on the friction coefficient. A new critical friction coefficient is exhibited below which contact forces remain bounded. Moreover a detailed analysis of the vector field nearby the singularity shows that the eventual divergence of the contact force does not call into question the model well-posedness.
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https://hal.inria.fr/inria-00073323
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Submitted on : Wednesday, May 24, 2006 - 12:32:30 PM
Last modification on : Friday, September 7, 2018 - 4:06:02 PM
Long-term archiving on: : Sunday, April 4, 2010 - 11:42:21 PM

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  • HAL Id : inria-00073323, version 1

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Frank Génot, Bernard Brogliato. New Results on Painlevé Paradoxes. RR-3366, INRIA. 1998. ⟨inria-00073323⟩

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