Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics]
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Rus. J. Nonlin. Dyn.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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. 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
Full-text PDF (2344 kB) Citations (15)
References:
PDF
HTML
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
\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{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:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Нелинейная динамика
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025