Abstract:
This paper is concerned with the rolling motion of a dynamically asymmetric unbalanced ball (Chaplygin top) in a gravitational field on a plane under the assumption that there is no slipping and spinning at the point of contact. We give a description of strange attractors existing in the system and discuss in detail the scenario of how one of them arises via a sequence of period-doubling bifurcations. In addition, we analyze the dynamics of the system in absolute space and show that in the presence of strange attractors in the system the behavior of the point of contact considerably depends on the characteristics of the attractor and can be both chaotic and nearly quasi-periodic.
Keywords:
Chaplygin top, nonholonomic constraint, rubber model, strange attractor, bifurcation, trajectory of the point of contact.
The work of A.V.Borisov (Introduction, Sections 1, 4 and 6) was carried out within the framework of the Grant of the Russian Science Foundation No. 15-12-20035. The work of A.O.Kazakov (Sections 2 and 3) was supported by the Basic Research Program at the National Research University Higher School of Economics (project 98) and by the RFBR grants No. 16-01-00364 and No. 14-01-00344. The work of E.N. Pivovarova (Section 5 and Conclusion) was supported by the Russian Foundation for Basic Research (project No. 15-08-09261-a).
Citation:
Alexey V. Borisov, Alexey O. Kazakov, Elena N. Pivovarova, “Regular and Chaotic Dynamics in the Rubber Model of a Chaplygin Top”, Regul. Chaotic Dyn., 21:7-8 (2016), 885–901
\Bibitem{BorKazPiv16}
\by Alexey V. Borisov, Alexey O. Kazakov, Elena N. Pivovarova
\paper Regular and Chaotic Dynamics in the Rubber Model of a Chaplygin Top
\jour Regul. Chaotic Dyn.
\yr 2016
\vol 21
\issue 7-8
\pages 885--901
\mathnet{http://mi.mathnet.ru/rcd234}
\crossref{https://doi.org/10.1134/S156035471607011X}
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