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., 2012, Volume 17, Issue 2, Pages 191–198 (Mi rcd339)  

This article is cited in 11 scientific papers (total in 11 papers)

Two Non-holonomic Integrable Problems Tracing Back to Chaplygin

Alexey V. Borisov, Ivan S. Mamaev

Institute of Computer Science, Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia

Abstract: The paper considers two new integrable systems which go back to Chaplygin. The systems consist of a spherical shell that rolls on a plane; within the shell there is a ball or Lagrange’s gyroscope. All necessary first integrals and an invariant measure are found. The solutions are shown to be expressed in terms of quadratures.

Keywords: non-holonomic constraint, integrability, invariant measure, gyroscope, quadrature, coupled rigid bodies

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 11.G34.31.0039
02.740.11.0195
14.740.11.0876
This research was supported by the Grant of the Government of the Russian Federation for state support of scientific research conducted under supervision of leading scientists in Russian educational institutions of higher professional education (contract no. 11.G34.31.0039) and the Federal target programme “Scientific and Scientific-Pedagogical Personnel of Innovative Russia”, measure 1.1. “Scientific-Educational Center Regular and Chaotic Dynamics” (project code 02.740.11.0195), measure 1.5 “Topology and Mechanics” (project code 14.740.11.0876).


DOI: https://doi.org/10.1134/S1560354712020074


Bibliographic databases:

MSC: 76M23, 34A05
Received: 14.08.2011
Accepted:29.11.2011
Language:

Citation: Alexey V. Borisov, Ivan S. Mamaev, “Two Non-holonomic Integrable Problems Tracing Back to Chaplygin”, Regul. Chaotic Dyn., 17:2 (2012), 191–198

Citation in format AMSBIB
\Bibitem{BorMam12}
\by Alexey V.~Borisov, Ivan S.~Mamaev
\paper Two Non-holonomic Integrable Problems Tracing Back to Chaplygin
\jour Regul. Chaotic Dyn.
\yr 2012
\vol 17
\issue 2
\pages 191--198
\mathnet{http://mi.mathnet.ru/rcd339}
\crossref{https://doi.org/10.1134/S1560354712020074}
\zmath{https://zbmath.org/?q=an:1252.76056}


Linking options:
  • http://mi.mathnet.ru/eng/rcd339
  • http://mi.mathnet.ru/eng/rcd/v17/i2/p191

    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. Alexey V. Borisov, Ivan S. Mamaev, Ivan A. Bizyaev, “The Hierarchy of Dynamics of a Rigid Body Rolling without Slipping and Spinning on a Plane and a Sphere”, Regul. Chaotic Dyn., 18:3 (2013), 277–328  mathnet  crossref  mathscinet  zmath
    2. S. V. Bolotin, T. V. Popova, “On the Motion of a Mechanical System Inside a Rolling Ball”, Regul. Chaotic Dyn., 18:1-2 (2013), 159–165  mathnet  crossref  mathscinet  zmath
    3. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Ierarkhiya dinamiki pri kachenii tverdogo tela bez proskalzyvaniya i vercheniya po ploskosti i sfere”, Nelineinaya dinam., 9:2 (2013), 141–202  mathnet
    4. I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Dinamika negolonomnykh sistem, sostoyaschikh iz sfericheskoi obolochki s podvizhnym tverdym telom vnutri”, Nelineinaya dinam., 9:3 (2013), 547–566  mathnet
    5. Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Dynamics of Nonholonomic Systems Consisting of a Spherical Shell with a Moving Rigid Body Inside”, Regul. Chaotic Dyn., 19:2 (2014), 198–213  mathnet  crossref  mathscinet  zmath
    6. Alexander A. Kilin, Elena N. Pivovarova, Tatyana B. Ivanova, “Spherical Robot of Combined Type: Dynamics and Control”, Regul. Chaotic Dyn., 20:6 (2015), 716–728  mathnet  crossref  mathscinet  adsnasa
    7. Pantelis A. Damianou, Hervé Sabourin, Pol Vanhaecke, “Intermediate Toda Systems”, Regul. Chaotic Dyn., 20:3 (2015), 277–292  mathnet  crossref  mathscinet  zmath  adsnasa
    8. A. A. Kilin, Yu. L. Karavaev, “Eksperimentalnye issledovaniya dinamiki sfericheskogo robota kombinirovannogo tipa”, Nelineinaya dinam., 11:4 (2015), 721–734  mathnet
    9. Ivanova T.B. Kilin A.A. Pivovarova E.N., “Controlled Motion of a Spherical Robot With Feedback. i”, J. Dyn. Control Syst., 24:3 (2018), 497–510  crossref  mathscinet  zmath  isi  scopus
    10. Ivanova T.B. Kilin A.A. Pivovarova E.N., “Control of the Rolling Motion of a Spherical Robot on An Inclined Plane”, Dokl. Phys., 63:10 (2018), 435–440  mathnet  crossref  isi  scopus
    11. Ivanova T.B., Kilin A.A., Pivovarova E.N., “Controlled Motion of a Spherical Robot of Pendulum Type on An Inclined Plane”, Dokl. Phys., 63:7 (2018), 302–306  mathnet  crossref  isi  scopus
  • Number of views:
    This page:15

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