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

    2010, Vol. 6, No. 4, pp.  829-854

    Author(s): Bolsinov A. V., Borisov A. V., Mamaev I. S.

    Hamiltonisation problem for non-holonomic systems, both integrable and non-integrable, is considered. This question is important for qualitative analysis of such systems and allows one to determine possible dynamical effects. The first part is devoted to the representation of integrable systems in a conformally Hamiltonian form. In the second part, the existence of a conformally Hamiltonian representation in a neighbourhood of a periodic solution is proved for an arbitrary measure preserving system (including integrable). General consructions are always illustrated by examples from non-holonomic mechanics.
    Keywords: conformally Hamiltonian system, nonholonomic system, invariant measure, periodic trajectory, invariant torus, integrable system
    Citation: Bolsinov A. V., Borisov A. V., Mamaev I. S., Hamiltonisation of non-holonomic systems in the neighborhood of invariant manifolds, Rus. J. Nonlin. Dyn., 2010, Vol. 6, No. 4, pp.  829-854

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