Regular and Chaotic Dynamics

, Volume 18, Issue 1–2, pp 144–158 | Cite as

How to control the Chaplygin ball using rotors. II

  • Alexey V. Borisov
  • Alexander A. Kilin
  • Ivan S. Mamaev
Article

Abstract

In our earlier paper [3] we examined the problem of control of a balanced dynamically nonsymmetric sphere with rotors with no-slip condition at the point of contact. In this paper we investigate the controllability of a ball in the presence of friction. We also study the problem of the existence and stability of singular dissipation-free periodic solutions for a free ball in the presence of friction forces. The issues of constructive realization of the proposed algorithms are discussed.

Keywords

non-holonomic constraint control dry friction viscous friction stability periodic solutions 

MSC2010 numbers

37J60 37J35 70E18 70F25 70H45 

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Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  • Alexey V. Borisov
    • 1
    • 2
    • 3
  • Alexander A. Kilin
    • 1
    • 2
    • 3
  • Ivan S. Mamaev
    • 1
    • 2
    • 3
  1. 1.Institute of Computer Science; Laboratory of Nonlinear Analysis and the Design of New Types of VehiclesUdmurt State UniversityIzhevskRussia
  2. 2.A.A. Blagonravov Mechanical Engineering Research Institute of RASMoscowRussia
  3. 3.Institute of Mathematics and Mechanics of the Ural Branch of RASEkaterinburgRussia

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