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Reports Year : 1998

New Results on Painlevé Paradoxes

Frank Génot
  • Function : Author
Bernard Brogliato


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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Dates and versions

inria-00073323 , version 1 (24-05-2006)


  • HAL Id : inria-00073323 , version 1


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