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Regular and Chaotic Dynamics, 2016, Volume 21, Issue 7-8, Pages 885–901
DOI: https://doi.org/10.1134/S156035471607011X (Mi rcd234) 		 
This article is cited in 12 scientific papers (total in 12 papers)

Regular and Chaotic Dynamics in the Rubber Model of a Chaplygin Top

Alexey V. Borisova, Alexey O. Kazakovb, Elena N. Pivovarovaa

a Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia
b National Research University Higher School of Economics, ul. Bolshaya Pecherskaya 25/12, Nizhny Novgorod, 603155 Russia
Citations (12)
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DOI: https://doi.org/10.1134/S156035471607011X
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.
Funding agency Grant number
Russian Science Foundation 15-12-20035
Ministry of Education and Science of the Russian Federation 98
Russian Foundation for Basic Research 16-01-00364
14-01-00344
15-08-09261-a
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).
Received: 21.11.2016
Accepted: 06.12.2016
Bibliographic databases:
Document Type: Article
MSC: 37J60, 37G35, 70E18
Language: English
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
Citation in format AMSBIB
\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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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85016012678}
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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