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Regul. Chaotic Dyn., 2016, Volume 21, Issue 7-8, Pages 939–954 (Mi rcd238)  

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

Spiral Chaos in the Nonholonomic Model of a Chaplygin Top

Alexey V. Borisova, Alexey O. Kazakovb, Igor R. Sataevac

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
c Institute of Radio Engineering and Electronics RAS, Saratov Branch ul. Zelenaya 38, Saratov, 410019 Russia

Abstract: This paper presents a numerical study of the chaotic dynamics of a dynamically asymmetric unbalanced ball (Chaplygin top) rolling on a plane. It is well known that the dynamics of such a system reduces to the investigation of a three-dimensional map, which in the general case has no smooth invariant measure. It is shown that homoclinic strange attractors of discrete spiral type (discrete Shilnikov type attractors) arise in this model for certain parameters. From the viewpoint of physical motions, the trace of the contact point of a Chaplygin top on a plane is studied for the case where the phase trajectory sweeps out a discrete spiral attractor. Using the analysis of the trajectory of this trace, a conclusion is drawn about the influence of “strangeness” of the attractor on the motion pattern of the top.

Keywords: nonholonomic constraint, spiral chaos, discrete spiral attractor

Funding Agency Grant Number
Russian Foundation for Basic Research 15-08-09261-a
14-01-00344
Ministry of Education and Science of the Russian Federation 98
Russian Science Foundation 15-12-20035
Dynasty Foundation
The work of A.V.Borisov (Introduction, Section 2 and Conclusion) was carried out within the framework of the state assignment for institutions of higher education and supported by the RFBR grant No. 15-08-09261-a. The work of A.O.Kazakov (Sections 1 and 5) was supported by the Basic Research Program at the National Research University Higher School of Economics (project 98), by the Dynasty Foundation, and by the RFBR grant No. 14-01-00344. The work of I.R. Sataev (Sections 3 and 4) was supported by the RSF grant No. 15-12-20035.


DOI: https://doi.org/10.1134/S1560354716070157

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Bibliographic databases:

MSC: 37J60, 37N15, 37G35, 70E18, 70F25, 70H45
Received: 12.10.2016
Accepted:29.11.2016
Language:

Citation: 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

Citation in format AMSBIB
\Bibitem{BorKazSat16}
\by Alexey V. Borisov, Alexey O. Kazakov, Igor R. Sataev
\paper Spiral Chaos in the Nonholonomic Model of a Chaplygin Top
\jour Regul. Chaotic Dyn.
\yr 2016
\vol 21
\issue 7-8
\pages 939--954
\mathnet{http://mi.mathnet.ru/rcd238}
\crossref{https://doi.org/10.1134/S1560354716070157}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000403091800015}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85015982180}


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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. 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  mathnet  crossref
    2. 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
    3. I. R. Garashchuk, D. I. Sinelshchikov, N. 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
    4. S. 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
    5. S. P. Kuznetsov, P. V. Kuptsov, “Lyapunov Analysis of Strange Pseudohyperbolic Attractors: Angles Between Tangent Subspaces, Local Volume Expansion and Contraction”, Regul. Chaotic Dyn., 23:7-8 (2018), 908–932  mathnet  crossref
    6. V. Putkaradze, S. Rogers, “On the dynamics of a rolling ball actuated by internal point masses”, Meccanica, 53:15 (2018), 3839–3868  crossref  mathscinet  isi  scopus
    7. A. S. Conchenko, V S. Conchenko, V O. Kazakovt, A. D. Kozlov, “Elements of contemporary theory of dynamical chaos: a tutorial. Part I. Pseudohyperbolic attractors”, Int. J. Bifurcation Chaos, 28:11 (2018), 1830036  crossref  mathscinet  isi  scopus
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