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Nelin. Dinam., 2016, Volume 12, Number 2, Pages 235–250 (Mi nd524)  

This article is cited in 2 scientific papers (total in 2 papers)

Original papers

Scenarios of transition to chaos in the nonholonomic model of a Chaplygin top

I. R. Sataevab, A. O. Kazakovcdb

a Kotel’nikov’s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, Zelenaya 38, Saratov, 410019, Russia
b Udmurt State University, Universitetskaya 1, Izhevsk, 426034 Russia
c Higher School of Economics National Research University, 25/12 Bolshaya Pecherskaya St., Nizhny Novgorod, 603155, Russia
d Lobachevsky State University of Nizhny Novgorod, 23 Prospekt Gagarina, Nizhny Novgorod, 603950, Russia

Abstract: We study the dynamics in the Suslov problem which describes the motion of a heavy rigid body with a fixed point subject to a nonholonomic constraint, which is expressed by the condition that the projection of angular velocity onto the body-fixed axis is equal to zero. Depending on the system parameters, we find cases of regular (in particular, integrable) motions and, using a new method for constructing charts of Lyapunov exponents, detect different types of chaotic behavior such as conservative chaos, strange attractors and mixed dynamics, which are typical of reversible systems. In the paper we also examine the phenomenon of reversal, which was observed previously in the motion of Celtic stones.

Keywords: nonholonomic model, Chaplygin top, Afraimovich – Shilnikov torus-breakdown, cascade of period-doubling bifurcations, scenario of period doublings of tori, figure-eight attractor

Funding Agency Grant Number
Russian Science Foundation 15-12-20035
National Research University Higher School of Economics 98
Russian Foundation for Basic Research 15-08-09261-а
15-38-20879 мол_а_вед
14-01-00344


Full text: PDF file (1565 kB)
References: PDF file   HTML file
UDC: 517.925 + 517.93
MSC: 37J60, 37N15, 37G35, 70E18, 70F25, 70H45
Received: 04.03.2016
Revised: 20.05.2016

Citation: I. R. Sataev, A. O. Kazakov, “Scenarios of transition to chaos in the nonholonomic model of a Chaplygin top”, Nelin. Dinam., 12:2 (2016), 235–250

Citation in format AMSBIB
\Bibitem{SatKaz16}
\by I.~R.~Sataev, A.~O.~Kazakov
\paper Scenarios of transition to chaos in the nonholonomic model of a Chaplygin top
\jour Nelin. Dinam.
\yr 2016
\vol 12
\issue 2
\pages 235--250
\mathnet{http://mi.mathnet.ru/nd524}
\elib{http://elibrary.ru/item.asp?id=26193560}


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