Hamiltonization of non-holonomic systems in the neighborhood of invariant manifolds

Article

Abstract

The problem of Hamiltonization of non-holonomic systems, both integrable and non-integrable, is considered. This question is important in the qualitative analysis of such systems and it enables one to determine possible dynamical effects. The first part of the paper is devoted to representing integrable systems in a conformally Hamiltonian form. In the second part, the existence of a conformally Hamiltonian representation in a neighborhood of a periodic solution is proved for an arbitrary (including integrable) system preserving an invariant measure. Throughout the paper, general constructions are illustrated by examples in non-holonomic mechanics.

Keywords

conformally Hamiltonian system non-holonomic system invariant measure periodic trajectory invariant torus integrable system 

MSC2010 numbers

37Jxx 

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Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  • A. V. Bolsinov
    • 1
    • 2
  • A. V. Borisov
    • 2
  • I. S. Mamaev
    • 2
  1. 1.School of MathematicsLoughborough University LoughboroughLeicestershireUK
  2. 2.Institute of Computer ScienceUdmurt State UniversityIzhevskRussia

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