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Bifurcations and Periodic Motion Induced by the Painlevé Paradox

Remco Leine 1 Bernard Brogliato 1
1 BIP - Biped Robot
Inria Grenoble - Rhône-Alpes
Abstract : In this report we study the periodic motion and bifurcations of the Frictional Bounce Model, which consists of an object with normal and tangential degrees of freedom that comes in contact with a rigid surface. The Frictional Bounce Model contains the basic mechanism for a hopping phenomenon observed in many practical applications. We will show that the hopping or bouncing motion in this type of systems is closely related to the Painlevé paradox. A dynamical system exhibiting the Painlevé paradox has nonuniqueness and nonexistence of solutions in certain sliding modes. Furthermore, we will show that this type of systems can exhibit the Painlevé paradox for physically realistic values of the friction coefficient.
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Submitted on : Tuesday, May 23, 2006 - 8:15:32 PM
Last modification on : Friday, February 4, 2022 - 3:23:55 AM
Long-term archiving on: : Tuesday, February 22, 2011 - 11:01:44 AM


  • HAL Id : inria-00072265, version 1



Remco Leine, Bernard Brogliato. Bifurcations and Periodic Motion Induced by the Painlevé Paradox. [Research Report] RR-4322, INRIA. 2001. ⟨inria-00072265⟩



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