Regular and Chaotic 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


Regul. Chaotic Dyn.:
Year:
Volume:
Issue:
Page:
Find




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

Regular and Chaotic Dynamics, 2016, Volume 21, Issue 7-8, Pages 939–954
DOI: https://doi.org/10.1134/S1560354716070157 (Mi rcd238) 		 
This article is cited in 22 scientific papers (total in 22 papers)

Spiral Chaos in the Nonholonomic Model of a Chaplygin Top

Alexey V. Borisova, Alexey O. Kazakovb, Igor R. Sataevac

a Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia
b National Research University Higher School of Economics, ul. Bolshaya Pecherskaya 25/12, Nizhny Novgorod, 603155 Russia
c Institute of Radio Engineering and Electronics RAS, Saratov Branch ul. Zelenaya 38, Saratov, 410019 Russia
Citations (22)
References:
PDF
HTML
DOI: https://doi.org/10.1134/S1560354716070157
Abstract: This paper presents a numerical study of the chaotic dynamics of a dynamically asymmetric unbalanced ball (Chaplygin top) rolling on a plane. It is well known that the dynamics of such a system reduces to the investigation of a three-dimensional map, which in the general case has no smooth invariant measure. It is shown that homoclinic strange attractors of discrete spiral type (discrete Shilnikov type attractors) arise in this model for certain parameters. From the viewpoint of physical motions, the trace of the contact point of a Chaplygin top on a plane is studied for the case where the phase trajectory sweeps out a discrete spiral attractor. Using the analysis of the trajectory of this trace, a conclusion is drawn about the influence of “strangeness” of the attractor on the motion pattern of the top.
Keywords: nonholonomic constraint, spiral chaos, discrete spiral attractor.
Funding agency Grant number
Russian Foundation for Basic Research 15-08-09261-a
14-01-00344
Ministry of Education and Science of the Russian Federation 98
Russian Science Foundation 15-12-20035
Dynasty Foundation
The work of A.V.Borisov (Introduction, Section 2 and Conclusion) was carried out within the framework of the state assignment for institutions of higher education and supported by the RFBR grant No. 15-08-09261-a. The work of A.O.Kazakov (Sections 1 and 5) was supported by the Basic Research Program at the National Research University Higher School of Economics (project 98), by the Dynasty Foundation, and by the RFBR grant No. 14-01-00344. The work of I.R. Sataev (Sections 3 and 4) was supported by the RSF grant No. 15-12-20035.
Received: 12.10.2016
Accepted: 29.11.2016
Bibliographic databases:
Document Type: Article
MSC: 37J60, 37N15, 37G35, 70E18, 70F25, 70H45
Language: English
Citation: 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
Citation in format AMSBIB
\Bibitem{BorKazSat16}
\by Alexey V. Borisov, Alexey O. Kazakov, Igor R. Sataev
\paper Spiral Chaos in the Nonholonomic Model of a Chaplygin Top
\jour Regul. Chaotic Dyn.
\yr 2016
\vol 21
\issue 7-8
\pages 939--954
\mathnet{http://mi.mathnet.ru/rcd238}
\crossref{https://doi.org/10.1134/S1560354716070157}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000403091800015}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85015982180}
Linking options:
  • https://www.mathnet.ru/eng/rcd238
  • https://www.mathnet.ru/eng/rcd/v21/i7/p939
    • This publication is cited in the following 22 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024