Regular and Chaotic Dynamics

, Volume 21, Issue 1, pp 136–146 | Cite as

Dynamics of the Chaplygin sleigh on a cylinder

  • Ivan A. Bizyaev
  • Alexey V. Borisov
  • Ivan S. Mamaev
Article

Abstract

This paper is concerned with the motion of the Chaplygin sleigh on the surface of a circular cylinder. In the case of inertial motion, the problem reduces to the study of the dynamical system on a (two-dimensional) torus and to the classification of singular points. Particular cases in which the system admits an invariant measure are found.

In the case of a balanced and dynamically symmetric Chaplygin sleigh moving in a gravitational field it is shown that on the average the system has no drift along the vertical.

Keywords

Chaplygin sleigh invariant measure nonholonomic mechanics 

MSC2010 numbers

37J60 37C10 

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Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  • Ivan A. Bizyaev
    • 1
  • Alexey V. Borisov
    • 1
  • Ivan S. Mamaev
    • 1
  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia

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