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Regul. Chaotic Dyn., 2016, Volume 21, Issue 7-8, Pages 885–901 (Mi rcd234)  

This article is cited in 7 scientific papers (total in 7 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

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).


DOI: https://doi.org/10.1134/S156035471607011X

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Bibliographic databases:

Document Type: Article
MSC: 37J60, 37G35, 70E18
Received: 21.11.2016
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}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000403091800011}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85016012678}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Alexander P. Ivanov, “On Final Motions of a Chaplygin Ball on a Rough Plane”, Regul. Chaotic Dyn., 21:7-8 (2016), 804–810  mathnet  crossref
    2. Alexey V. Borisov, Alexey O. Kazakov, Igor R. Sataev, “Spiral Chaos in the Nonholonomic Model of a Chaplygin Top”, Regul. Chaotic Dyn., 21:7-8 (2016), 939–954  mathnet  crossref
    3. Alexander A. Kilin, Elena N. Pivovarova, “The Rolling Motion of a Truncated Ball Without Slipping and Spinning on a Plane”, Regul. Chaotic Dyn., 22:3 (2017), 298–317  mathnet  crossref  mathscinet
    4. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics”, Russian Math. Surveys, 72:5 (2017), 783–840  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    5. S. P. Kuznetsov, “Regular and chaotic motions of the Chaplygin sleigh with periodically switched location of nonholonomic constraint”, EPL, 118:1 (2017), 10007  crossref  mathscinet  isi  scopus
    6. Ivan R. Garashchuk, Dmitry I. Sinelshchikov, Nikolay A. Kudryashov, “Nonlinear Dynamics of a Bubble Contrast Agent Oscillating near an Elastic Wall”, Regul. Chaotic Dyn., 23:3 (2018), 257–272  mathnet  crossref  mathscinet  adsnasa
    7. Sergey P. Kuznetsov, “Regular and Chaotic Dynamics of a Chaplygin Sleigh due to Periodic Switch of the Nonholonomic Constraint”, Regul. Chaotic Dyn., 23:2 (2018), 178–192  mathnet  crossref
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