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Regular and Chaotic Dynamics

, Volume 21, Issue 2, pp 204–231 | Cite as

Dynamics of a rolling and sliding disk in a plane. Asymptotic solutions, stability and numerical simulations

  • Maria PrzybylskaEmail author
  • Stefan Rauch-Wojciechowski
Article

Abstract

We present a qualitative analysis of the dynamics of a rolling and sliding disk in a horizontal plane. It is based on using three classes of asymptotic solutions: straight-line rolling, spinning about a vertical diameter and tumbling solutions. Their linear stability analysis is given and it is complemented with computer simulations of solutions starting in the vicinity of the asymptotic solutions. The results on asymptotic solutions and their linear stability apply also to an annulus and to a hoop.

Keywords

rigid body nonholonomic mechanics rolling disk sliding disk 

MSC2010 numbers

37J60 37J25 70G45 

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Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Institute of PhysicsUniversity of Zielona GóraZielona GóraPoland
  2. 2.Department of MathematicsLinköping UniversityLinköpingSweden

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