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Regular and Chaotic Dynamics, 2011, Volume 16, Issue 6, Pages 663–670
DOI: https://doi.org/10.1134/S1560354711060074
(Mi rcd462)
 

This article is cited in 9 scientific papers (total in 9 papers)

Routh Symmetry in the Chaplygin’s Rolling Ball

Byungsoo Kim

INRS-ETE, Quebec, G1K 9A9, Canada
Citations (9)
Abstract: The Routh integral in the symmetric Chaplygin’s rolling ball has been regarded as a mysterious conservation law due to its interesting form of I1I3+mIs,sΩ3. In this paper, a new form of the Routh integral is proposed as a Noether’s pairing form of a conservation law. An explicit symmetry vector for the Routh integral is proved to associate the conserved quantity with the invariance of the Lagrangian function under the rollingly constrained nonholonomic variation. Then, the form of the Routh symmetry vector is discussed for its origin as the linear combination of the configurational vectors.
Keywords: non-holonomic system, Noether symmetry, integrable system, Lagrange–D’Alembert equations.
Received: 21.06.2011
Accepted: 17.08.2011
Bibliographic databases:
Document Type: Article
MSC: 37J60, 37J35, 70F25
Language: English
Citation: Byungsoo Kim, “Routh Symmetry in the Chaplygin’s Rolling Ball”, Regul. Chaotic Dyn., 16:6 (2011), 663–670
Citation in format AMSBIB
\Bibitem{Kim11}
\by Byungsoo Kim
\paper Routh Symmetry in the Chaplygin’s Rolling Ball
\jour Regul. Chaotic Dyn.
\yr 2011
\vol 16
\issue 6
\pages 663--670
\mathnet{http://mi.mathnet.ru/rcd462}
\crossref{https://doi.org/10.1134/S1560354711060074}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2864540}
\zmath{https://zbmath.org/?q=an:1253.37065}
Linking options:
  • https://www.mathnet.ru/eng/rcd462
  • https://www.mathnet.ru/eng/rcd/v16/i6/p663
  • This publication is cited in the following 9 articles:
    1. Miguel D. Bustamante, Peter Lynch, “Nonholonomic Noetherian Symmetries and Integrals of the Routh Sphere and the Chaplygin Ball”, Regul. Chaotic Dyn., 24:5 (2019), 511–524  mathnet  crossref  mathscinet
    2. François Gay-Balmaz, Vakhtang Putkaradze, “On Noisy Extensions of Nonholonomic Constraints”, J Nonlinear Sci, 26:6 (2016), 1571  crossref
    3. A. V. Borisov, I. S. Mamaev, “Simmetrii i reduktsiya v negolonomnoi mekhanike”, Nelineinaya dinam., 11:4 (2015), 763–823  mathnet
    4. Alexey V. Borisov, Ivan S. Mamaev, “Symmetries and Reduction in Nonholonomic Mechanics”, Regul. Chaotic Dyn., 20:5 (2015), 553–604  mathnet  crossref  mathscinet  zmath
    5. Peter Lynch, Miguel D. Bustamante, “Quaternion Solution for the Rock’n’roller: Box Orbits, Loop Orbits and Recession”, Regul. Chaotic Dyn., 18:1-2 (2013), 166–183  mathnet  crossref  mathscinet  zmath
    6. 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
    7. Valery V. Kozlov, “The Euler–Jacobi–Lie Integrability Theorem”, Regul. Chaotic Dyn., 18:4 (2013), 329–343  mathnet  crossref  mathscinet  zmath
    8. 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
    9. 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
    Citing articles in Google Scholar: Russian citations, English citations
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