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Regular and Chaotic Dynamics

, Volume 22, Issue 3, pp 298–317 | Cite as

The rolling motion of a truncated ball without slipping and spinning on a plane

  • Alexander A. Kilin
  • Elena N. Pivovarova
Article
  • 50 Downloads

Abstract

This paper is concerned with the dynamics of a top in the form of a truncated ball as it moves without slipping and spinning on a horizontal plane about a vertical. Such a system is described by differential equations with a discontinuous right-hand side. Equations describing the system dynamics are obtained and a reduction to quadratures is performed. A bifurcation analysis of the system is made and all possible types of the top’s motion depending on the system parameters and initial conditions are defined. The system dynamics in absolute space is examined. It is shown that, except for some special cases, the trajectories of motion are bounded.

Keywords

integrable system system with discontinuity nonholonomic constraint bifurcation diagram absolute dynamics 

MSC2010 numbers

70E15 70E18 70E40 37Jxx 

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Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Udmurt State UniversityIzhevskRussia
  2. 2.Institute of Mathematics and Mechanics of the Ural Branch of RASEkaterinburgRussia

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