Regular and Chaotic Dynamics

, Volume 21, Issue 7–8, pp 939–954 | Cite as

Spiral chaos in the nonholonomic model of a Chaplygin top

  • Alexey V. Borisov
  • Alexey O. Kazakov
  • Igor R. Sataev
Nonlinear Dynamics & Mobile Robotics

Abstract

This paper presents a numerical study of the chaotic dynamics of a dynamically asymmetric unbalanced ball (Chaplygin top) rolling on a plane. It is well known that the dynamics of such a system reduces to the investigation of a three-dimensional map, which in the general case has no smooth invariant measure. It is shown that homoclinic strange attractors of discrete spiral type (discrete Shilnikov type attractors) arise in this model for certain parameters. From the viewpoint of physical motions, the trace of the contact point of a Chaplygin top on a plane is studied for the case where the phase trajectory sweeps out a discrete spiral attractor. Using the analysis of the trajectory of this trace, a conclusion is drawn about the influence of “strangeness” of the attractor on the motion pattern of the top.

Keywords

nonholonomic constraint spiral chaos discrete spiral attractor 

MSC2010 numbers

37J60 37N15 37G35 70E18 70F25 70H45 

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Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  • Alexey V. Borisov
    • 1
  • Alexey O. Kazakov
    • 2
  • Igor R. Sataev
    • 1
    • 3
  1. 1.Udmurt State UniversityIzhevskRussia
  2. 2.National Research University Higher School of EconomicsNizhny NovgorodRussia
  3. 3.Institute of Radio Engineering and Electronics RASSaratovRussia

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