Abstract:
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 the 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.
This research was supported by the Target Programmes for 2012–2014 (State contract 1.1248.2011, 1.7734.2013) and grant RFBR 13-01-12462-ofi_m. A. A. Kilin’s research was supported by the grant of the President of the Russian Federation for the Support of Young Russian Scientists–Doctors of Science (MD-2324.2013.1).
Citation:
Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “The Problem of Drift and Recurrence for the Rolling Chaplygin Ball”, Regul. Chaotic Dyn., 18:6 (2013), 832–859
\Bibitem{BorKilMam13}
\by Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev
\paper The Problem of Drift and Recurrence for the Rolling Chaplygin Ball
\jour Regul. Chaotic Dyn.
\yr 2013
\vol 18
\issue 6
\pages 832--859
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\crossref{https://doi.org/10.1134/S1560354713060166}
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