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    The problem of drift and recurrence for the rolling Chaplygin ball

    2013, Vol. 9, No. 4, pp.  721-754

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

    We investigate the motion of the point of contact (absolute dynamics) in the integrable problem of the Chaplygin ball rolling on a plane. Although the velocity of the point of contact is a given vector function of variables of a reduced system, it is impossible to apply standard methods of the theory of integrable Hamiltonian systems due to the absence of an appropriate conformally Hamiltonian representation for an unreduced system. For a complete analysis we apply the standard analytical approach, due to Bohl and Weyl, and develop topological methods of investigation. In this way we obtain conditions for boundedness and unboundedness of the trajectories of the contact point.
    Keywords: nonholonomic constraint, absolute dynamics, bifurcation diagram, bifurcation complex, drift, resonance, invariant torus
    Citation: Borisov A. V., Kilin A. A., Mamaev I. S., The problem of drift and recurrence for the rolling Chaplygin ball, Rus. J. Nonlin. Dyn., 2013, Vol. 9, No. 4, pp.  721-754
    DOI:10.20537/nd1304009


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