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


Regul. Chaotic Dyn., 2014, Volume 19, Issue 2, Pages 185–197 (Mi rcd124)  

This article is cited in 6 scientific papers (total in 6 papers)

On the Lie Integrability Theorem for the Chaplygin Ball

Andrey V.  Tsiganov

St.Petersburg State University, ul. Ulyanovskaya 1, St. Petersburg, 198504 Russia

Abstract: The necessary number of commuting vector fields for the Chaplygin ball in the absolute space is constructed. We propose to get these vector fields in the framework of the Poisson geometry similar to Hamiltonian mechanics.

Keywords: nonholonomic dynamical system, Poisson bracket, Lie theorem, Chaplygin ball

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00061_
This work was partially supported by RFBR grant 13-01-00061.


DOI: https://doi.org/10.1134/S1560354714020038

References: PDF file   HTML file

Bibliographic databases:

MSC: 37J60, 37J35, 70E18, 53D17
Received: 04.12.2013
Accepted:09.01.2014
Language:

Citation: Andrey V. Tsiganov, “On the Lie Integrability Theorem for the Chaplygin Ball”, Regul. Chaotic Dyn., 19:2 (2014), 185–197

Citation in format AMSBIB
\Bibitem{Tsi14}
\by Andrey~V. ~Tsiganov
\paper On the Lie Integrability Theorem for the Chaplygin Ball
\jour Regul. Chaotic Dyn.
\yr 2014
\vol 19
\issue 2
\pages 185--197
\mathnet{http://mi.mathnet.ru/rcd124}
\crossref{https://doi.org/10.1134/S1560354714020038}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3189256}
\zmath{https://zbmath.org/?q=an:1335.37046}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000334198000003}


Linking options:
  • http://mi.mathnet.ru/eng/rcd124
  • http://mi.mathnet.ru/eng/rcd/v19/i2/p185

    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. A. Tsiganov, “Poisson structures for two nonholonomic systems with partially reduced symmetries”, J. Geom. Mech., 6:3 (2014), 417–440  crossref  mathscinet  zmath  isi  scopus
    2. Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “Dynamics and Control of an Omniwheel Vehicle”, Regul. Chaotic Dyn., 20:2 (2015), 153–172  mathnet  crossref  mathscinet  zmath  adsnasa
    3. Andrey V. Tsiganov, “On Integrable Perturbations of Some Nonholonomic Systems”, SIGMA, 11 (2015), 085, 19 pp.  mathnet  crossref
    4. I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Hamiltonization of elementary nonholonomic systems”, Russ. J. Math. Phys., 22:4 (2015), 444–453  crossref  mathscinet  zmath  isi  scopus
    5. Andrey V. Tsiganov, “Hamiltonization and Separation of Variables for a Chaplygin Ball on a Rotating Plane”, Regul. Chaotic Dyn., 24:2 (2019), 171–186  mathnet  crossref
    6. Kurt M. Ehlers, Jair Koiller, “Cartan meets Chaplygin”, Theor. Appl. Mech., 46:1 (2019), 15–46  mathnet  crossref
  • Number of views:
    This page:80
    References:19

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2022