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

Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics]

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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2017, Volume 13, Number 2, Pages 277–297
DOI: https://doi.org/10.20537/nd1702009 (Mi nd565)

This article is cited in 15 scientific papers (total in 15 papers)

Translated papers

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

A. V. Borisov^a, A. O. Kazakov^b, E. N. Pivovarova^a

^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

Full-text PDF (2344 kB) Citations (15)

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

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

Received: 21.11.2017
Accepted: 06.12.2017

English version:
Regular and Chaotic Dynamics, 2016, Volume 21, Issue 7-8, Pages 885–901
DOI: https://doi.org/10.1134/S156035471607011X

Bibliographic databases:

Document Type: Article

UDC: 531.3

MSC: 37J60, 37G35, 70E18

Language: Russian

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

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\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{https://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{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85016012678}

Linking options:

https://www.mathnet.ru/eng/nd565

https://www.mathnet.ru/eng/nd/v13/i2/p277

This publication is cited in the following 15 articles:

Alexander A. Kilin, Elena N. Pivovarova, “Bifurcation analysis of the problem of a “rubber” ellipsoid of revolution rolling on a plane”, Nonlinear Dyn, 2024
Evgeniya A. Mikishanina, “Dynamics of the Chaplygin sphere with additional constraint”, Commun. Nonlinear Sci. Numer. Simul., 117 (2023), 106920–15
E. A. Mikishanina, “Dinamika kacheniya diska s naklonnoi skolzyaschei oporoi”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2021, no. 3, 45–56
Elizaveta M. Artemova, Yury L. Karavaev, Ivan S. Mamaev, Evgeny V. Vetchanin, “Dynamics of a Spherical Robot with Variable Moments of Inertia and a Displaced Center of Mass”, Regul. Chaotic Dyn., 25:6 (2020), 689–706
Alexey V. Borisov, Evgeniya A. Mikishanina, “Two Nonholonomic Chaotic Systems. Part II. On the Rolling of a Nonholonomic Bundle of Two Bodies”, Regul. Chaotic Dyn., 25:4 (2020), 392–400
Borislav Gajić, Božidar Jovanović, “Nonholonomic connections, time reparametrizations, and integrability of the rolling ball over a sphere”, Nonlinearity, 32:5 (2019), 1675
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
I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Dynamics of the Chaplygin ball on a rotating plane”, Russ. J. Math. Phys., 25:4 (2018), 423
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
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
Sergey P. Kuznetsov, “Regular and chaotic motions of the Chaplygin sleigh with periodically switched location of nonholonomic constraint”, EPL, 118:1 (2017), 10007
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
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
Alexander P. Ivanov, “On Final Motions of a Chaplygin Ball on a Rough Plane”, Regul. Chaotic Dyn., 21:7 (2016), 804–810
Alexey V. Borisov, Alexey O. Kazakov, Igor R. Sataev, “Spiral Chaos in the Nonholonomic Model of a Chaplygin Top”, Regul. Chaotic Dyn., 21:7 (2016), 939–954

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

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