Periodic Motion Induced by the Painlevé Paradox

  • R. I. Leine
  • B. Brogliato
  • H. Nijmeijer
Part of the International Centre for Mechanical Sciences book series (CISM, volume 444)


This chapter describes the periodic motion of the Frictional Impact Oscillator, which consists of an object with normal and tangential degrees of freedom that comes in contact with a rigid surface. The Frictional Impact Oscillator 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 non-uniqueness and non-existence 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.


Friction Coefficient Periodic Solution Periodic Motion Linear Complementarity Problem Normal Contact Force 
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Copyright information

© Springer-Verlag Wien 2004

Authors and Affiliations

  • R. I. Leine
    • 1
  • B. Brogliato
    • 2
  • H. Nijmeijer
    • 1
  1. 1.Eindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.INRIA Rhône-AlpesSaint IsmierFrance

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