Regular and Chaotic Dynamics

, Volume 19, Issue 1, pp 116–139 | Cite as

The dynamics of a rigid body with a sharp edge in contact with an inclined surface in the presence of dry friction

  • Ivan S. Mamaev
  • Tatiana B. Ivanova


In this paper we consider the dynamics of a rigid body with a sharp edge in contact with a rough plane. The body can move so that its contact point is fixed or slips or loses contact with the support. In this paper, the dynamics of the system is considered within three mechanical models which describe different regimes of motion. The boundaries of the domain of definition of each model are given, the possibility of transitions from one regime to another and their consistency with different coefficients of friction on the horizontal and inclined surfaces are discussed.


rod Painlevé paradox dry friction loss of contact frictional impact 

MSC2010 numbers

70F40 70E18 


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Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.Institute of Computer ScienceUdmurt State UniversityIzhevskRussia
  2. 2.Faculty of Physics and EnergeticsUdmurt State UniversityIzhevskRussia

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