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Nelin. Dinam., 2017, Volume 13, Number 2, Pages 277–297 (Mi nd565)  

This article is cited in 1 scientific paper (total in 1 paper)

Translated papers

Regular and chaotic dynamics in the rubber model of a Chaplygin top

A. V. Borisova, A. O. Kazakovb, E. N. Pivovarovaa

a Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034, Russia
b Higher School of Economics National Research University, 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 perioddoubling 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 Foundation for Basic Research 15-08-09261-a
16-51-10005 КО_а
Ministry of Education and Science of the Russian Federation 1.2404.2017/4.6
National Research University Higher School of Economics 90
Russian Science Foundation 15-12-20035
Dynasty Foundation


DOI: https://doi.org/10.20537/nd1702009

Full text: PDF file (2344 kB)
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English version:
Regular and Chaotic Dynamics, 2016, 21:7-8, 885–901

Document Type: Article
UDC: 531.3
MSC: 37J60, 37G35, 70E18
Received: 21.11.2017
Accepted:06.12.2017

Citation: A. V. Borisov, A. O. Kazakov, E. N. Pivovarova, “Regular and chaotic dynamics in the rubber model of a Chaplygin top”, Nelin. Dinam., 13:2 (2017), 277–297; Regular and Chaotic Dynamics, 21:7-8 (2016), 885–901

Citation in format AMSBIB
\Bibitem{BorKazPiv17}
\by A.~V.~Borisov, A.~O.~Kazakov, E.~N.~Pivovarova
\paper Regular and chaotic dynamics in the rubber model of a Chaplygin top
\jour Nelin. Dinam.
\yr 2017
\vol 13
\issue 2
\pages 277--297
\mathnet{http://mi.mathnet.ru/nd565}
\crossref{https://doi.org/10.20537/nd1702009}
\elib{http://elibrary.ru/item.asp?id=29443382}
\transl
\jour Regular and Chaotic Dynamics
\yr 2016
\vol 21
\issue 7-8
\pages 885--901
\crossref{https://doi.org/10.1134/S156035471607011X}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85016012678}


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    This publication is cited in the following articles:
    1. Yu. L. Karavaev, A. V. Klekovkin, A. A. Kilin, “Dinamicheskaya model treniya kacheniya sfericheskikh tel po ploskosti bez proskalzyvaniya”, Nelineinaya dinam., 13:4 (2017), 599–609  mathnet  crossref  elib
  • Нелинейная динамика
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