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Nelin. Dinam., 2016, Volume 12, Number 2, Pages 263–287 (Mi nd526)  

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

Translated papers

Dynamics of the Suslov problem in a gravitational field: reversal and strange attractors

I. A. Bizyaeva, A. V. Borisova, A. O. Kazakovbcd

a Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
b Udmurt State University, Universitetskaya 1, Izhevsk, 426034 Russia
c Lobachevsky State University of Nizhny Novgorod, 23 Prospekt Gagarina, Nizhny Novgorod, 603950, Russia
d Higher School of Economics National Research University, 25/12 Bolshaya Pecherskaya St., Nizhny Novgorod, 603155, Russia

Abstract: In this paper, we present some results on chaotic dynamics in the Suslov problem which describe 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) behavior and detect various attracting sets (including strange attractors) that are typical of dissipative systems.We construct a chart of regimes with regions characterizing chaotic and regular regimes depending on the degree of conservativeness. We examine in detail the effect of reversal, which was observed previously in the motion of rattlebacks.

Keywords: Suslov problem, nonholonomic constraint, reversal, strange attractor

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
15-12-20035


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English version:
Regul. Chaotic Dyn., 2015, 20:5, 605–626

Bibliographic databases:

Document Type: Article
UDC: 517.925 + 517.93
MSC: 37J60, 37N15, 37G35, 70E18, 70F25, 70H45
Received: 14.08.2015
Revised: 17.09.2015

Citation: I. A. Bizyaev, A. V. Borisov, A. O. Kazakov, “Dynamics of the Suslov problem in a gravitational field: reversal and strange attractors”, Nelin. Dinam., 12:2 (2016), 263–287; Regul. Chaotic Dyn., 20:5 (2015), 605–626

Citation in format AMSBIB
\Bibitem{BizBorKaz16}
\by I.~A.~Bizyaev, A.~V.~Borisov, A.~O.~Kazakov
\paper Dynamics of the Suslov problem in a gravitational field: reversal and strange attractors
\jour Nelin. Dinam.
\yr 2016
\vol 12
\issue 2
\pages 263--287
\mathnet{http://mi.mathnet.ru/nd526}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3453983}
\elib{http://elibrary.ru/item.asp?id=26193562}
\transl
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 5
\pages 605--626
\crossref{https://doi.org/10.1134/S1560354715050056}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84983781383}


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    Translation

    This publication is cited in the following articles:
    1. 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
  • Нелинейная динамика
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