Russian Journal of Mathematical Physics

, Volume 22, Issue 4, pp 444–453 | Cite as

Hamiltonization of elementary nonholonomic systems

Article

Abstract

In this paper, we develop the method of Chaplygin’s reducing multiplier; using this method, we obtain a conformally Hamiltonian representation for three nonholonomic systems, namely, for the nonholonomic oscillator, for the Heisenberg system, and for the Chaplygin sleigh. Furthermore, in the case of oscillator and nonholonomic Chaplygin sleigh, we show that the problem reduces to the study of motion of a mass point (in a potential field) on a plane and, in the case of Heisenberg system, on the sphere. Moreover, we consider an example of a nonholonomic system (suggested by Blackall) to which one cannot apply the method of reducing multiplier.

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Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  • I. A. Bizyaev
    • 1
  • A. V. Borisov
    • 2
    • 3
  • I. S. Mamaev
    • 4
  1. 1.Udmurt State UniversityIzhevskRussia
  2. 2.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia
  3. 3.Udmurt State UniversityIzhevskRussia
  4. 4.Izhevsk State Technical UniversityIzhevskRussia

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