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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
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).


Bibliographic databases:

MSC: 76M23, 34A05
Received: 14.08.2011

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
\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

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    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
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