Geometrization of the Chaplygin reducing-multiplier theorem

    2013, Vol. 9, No. 4, pp.  627-640

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

    This paper develops the theory of the reducing multiplier for a special class of nonholonomic dynamical systems, when the resulting nonlinear Poisson structure is reduced to the Lie–Poisson bracket of the algebra $e(3)$. As an illustration, the Chaplygin ball rolling problem and the Veselova system are considered. In addition, an integrable gyrostatic generalization of the Veselova system is obtained.
    Keywords: nonholonomic dynamical system, Poisson bracket, Poisson structure, reducing multiplier, Hamiltonization, conformally Hamiltonian system, Chaplygin ball
    Citation: Bolsinov A. V., Borisov A. V., Mamaev I. S., Geometrization of the Chaplygin reducing-multiplier theorem, Rus. J. Nonlin. Dyn., 2013, Vol. 9, No. 4, pp.  627-640

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