Regular and Chaotic Dynamics

, Volume 21, Issue 7–8, pp 885–901 | Cite as

Regular and chaotic dynamics in the rubber model of a Chaplygin top

  • Alexey V. Borisov
  • Alexey O. Kazakov
  • Elena N. Pivovarova
Nonlinear Dynamics & Mobile Robotics

Abstract

This paper is concerned with the rolling motion of a dynamically asymmetric unbalanced ball (Chaplygin top) in a gravitational field on a plane under the assumption that there is no slipping and spinning at the point of contact. We give a description of strange attractors existing in the system and discuss in detail the scenario of how one of them arises via a sequence of period-doubling bifurcations. In addition, we analyze the dynamics of the system in absolute space and show that in the presence of strange attractors in the system the behavior of the point of contact considerably depends on the characteristics of the attractor and can be both chaotic and nearly quasi-periodic.

Keywords

Chaplygin top nonholonomic constraint rubber model strange attractor bifurcation trajectory of the point of contact 

MSC2010 numbers

37J60 37G35 70E18 

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Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  • Alexey V. Borisov
    • 1
  • Alexey O. Kazakov
    • 2
  • Elena N. Pivovarova
    • 1
  1. 1.Udmurt State UniversityIzhevskRussia
  2. 2.National Research University Higher School of EconomicsNizhny NovgorodRussia

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