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



Nelin. Dinam.:
Year:
Volume:
Issue:
Page:
Find






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


Nelin. Dinam., 2014, Volume 10, Number 3, Pages 361–380 (Mi nd450)  

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

Regular and chaotic attractors in the nonholonomic model of Chapygins ball

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

a Udmurt State University, Universitetskaya 1, Izhevsk, 426034, Russia
b Lobachevsky State University of Nizhny Novgorod, 23 Prospekt Gagarina, Nizhny Novgorod, 603950, Russia
c Saratov Branch of Kotelnikovs Institute of Radio-Engineering and Electronics of RAS, Zelenaya st. 38, Saratov, 410019, Russia

Abstract: We study both analytically and numerically the dynamics of an inhomogeneous ball on a rough horizontal plane under the infuence of gravity. A nonholonomic constraint of zero velocity at the point of contact of the ball with the plane is imposed. In the case of an arbitrary displacement of the center of mass of the ball, the system is nonintegrable without the property of phase volume conservation. We show that at certain parameter values the unbalanced ball exhibits the effect of reversal (the direction of the ball rotation reverses). Charts of dynamical regimes on the parameter plane are presented. The system under consideration exhibits diverse chaotic dynamics, in particular, the figure-eight chaotic attractor, which is a special type of pseudohyperbolic chaos.

Keywords: Chaplygins top, rolling without slipping, reversibility, involution, integrability, reverse, chart of dynamical regimes, strange attractor.

Full text: PDF file (1334 kB)
References: PDF file   HTML file

UDC: 517.925+517.93
MSC: 37J60, 37N15, 37G35, 70E18, 70F25, 70H45
Received: 26.08.2014
Revised: 07.09.2014

Citation: Alexey V. Borisov, Alexey O. Kazakov, Igor R. Sataev, “Regular and chaotic attractors in the nonholonomic model of Chapygins ball”, Nelin. Dinam., 10:3 (2014), 361–380

Citation in format AMSBIB
\Bibitem{BorKazSat14}
\by Alexey~V.~Borisov, Alexey~O.~Kazakov, Igor~R.~Sataev
\paper Regular and chaotic attractors in the nonholonomic model of Chapygins ball
\jour Nelin. Dinam.
\yr 2014
\vol 10
\issue 3
\pages 361--380
\mathnet{http://mi.mathnet.ru/nd450}


Linking options:
  • http://mi.mathnet.ru/eng/nd450
  • http://mi.mathnet.ru/eng/nd/v10/i3/p361

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


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

    This publication is cited in the following articles:
    1. I. R. Sataev, A. O. Kazakov, “Stsenarii perekhoda k khaosu v negolonomnoi modeli volchka Chaplygina”, Nelineinaya dinam., 12:2 (2016), 235–250  mathnet  elib
  • Number of views:
    This page:295
    Full text:72
    References:58

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019