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Nelin. Dinam., 2008, Volume 4, Number 3, Pages 223–280 (Mi nd235)  

This article is cited in 15 scientific papers (total in 17 papers)

Conservation laws, hierarchy of dynamics and explicit integration of nonholonomic systems

A. V. Borisovabc, I. S. Mamaevabc

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Udmurt State University
c Institute of Computer Science

Abstract: This paper can be regarded as a continuation of our previous work [70, 71] on the hierarchy of the dynamical behavior of nonholonomic systems. We consider different mechanical systems with nonholonomic constraints; in particular, we examine the existence of tensor invariants (laws of conservation) and their connection with the behavior of a system. Considerable attention is given to the possibility of conformally Hamiltonian representation of the equations of motion, which is mainly used for the integration of the considered systems.

Keywords: nonholonomic systems, implementation of constraints, conservation laws, hierarchy of dynamics, explicit integration.

Full text: PDF file (503 kB)

Document Type: Article
UDC: 531.38
MSC: 34D20, 70E40, 37J35
Received: 13.06.2008

Citation: A. V. Borisov, I. S. Mamaev, “Conservation laws, hierarchy of dynamics and explicit integration of nonholonomic systems”, Nelin. Dinam., 4:3 (2008), 223–280

Citation in format AMSBIB
\Bibitem{BorMam08}
\by A.~V.~Borisov, I.~S.~Mamaev
\paper Conservation laws, hierarchy of dynamics and explicit integration of nonholonomic systems
\jour Nelin. Dinam.
\yr 2008
\vol 4
\issue 3
\pages 223--280
\mathnet{http://mi.mathnet.ru/nd235}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Bolsinov, A. V. Borisov, I. S. Mamaev, “Topology and stability of integrable systems”, Russian Math. Surveys, 65:2 (2010), 259–318  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. V. F. Zhuravlev, A. V. Borisov, “V. F. Zhuravlev. Otklik na statyu A. V. Borisova i I. S. Mamaeva «Zakony sokhraneniya, ierarkhiya dinamiki i yavnoe integrirovanie negolonomnykh sistem». Otvet A. V. Borisova”, Nelineinaya dinam., 6:2 (2010), 365–369  mathnet
    3. A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Gamiltonovost i integriruemost zadachi Suslova”, Nelineinaya dinam., 6:1 (2010), 127–142  mathnet
    4. A. V. Borisov, “Otvet V. F. Zhuravlevu”, Nelineinaya dinam., 6:4 (2010), 897–901  mathnet
    5. A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Kak upravlyat sharom Chaplygina pri pomoschi rotorov”, Nelineinaya dinam., 8:2 (2012), 289–307  mathnet
    6. A. V. Tsyganov, “O puassonovykh strukturakh, voznikayuschikh pri rassmotrenii shara Chaplygina i ego obobschenii”, Nelineinaya dinam., 8:2 (2012), 345–353  mathnet
    7. A. V. Bolsinov, A. V. Borisov, I. S. Mamaev, “Kachenie bez vercheniya shara po ploskosti: otsutstvie invariantnoi mery v sisteme s polnym naborom integralov”, Nelineinaya dinam., 8:3 (2012), 605–616  mathnet
    8. Alexey V. Borisov, Ivan S. Mamaev, Dmitrii V. Treschev, “Rolling of a rigid body without slipping and spinning: kinematics and dynamics”, J. Appl. Nonlinear Dyn., 2:2 (2013), 161–173  mathnet  crossref
    9. 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
    10. I. A. Bizyaev, A. O. Kazakov, “Integriruemost i stokhastichnost nekotorykh zadach negolonomnoi mekhaniki”, Nelineinaya dinam., 9:2 (2013), 257–265  mathnet
    11. A. O. Kazakov, “Fenomeny khaoticheskoi dinamiki v zadache o kachenii rok-n-rollera bez vercheniya”, Nelineinaya dinam., 9:2 (2013), 309–325  mathnet
    12. 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
    13. A. V. Bolsinov, A. V. Borisov, I. S. Mamaev, “Geometrizatsiya teoremy Chaplygina o privodyaschem mnozhitele”, Nelineinaya dinam., 9:4 (2013), 627–640  mathnet
    14. A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Problema dreifa i vozvraschaemosti pri kachenii shara Chaplygina”, Nelineinaya dinam., 9:4 (2013), 721–754  mathnet
    15. Bizyaev I.A., Borisov A.V., Mamaev I.S., “The Dynamics of Nonholonomic Systems Consisting of a Spherical Shell With a Moving Rigid Body Inside”, Regul. Chaotic Dyn., 19:2 (2014), 198–213  crossref  isi
    16. I. A. Bizyaev, A. V. Bolsinov, A. V. Borisov, I. S. Mamaev, “Topology and bifurcations in nonholonomic mechanics”, International Journal of Bifurcation and Chaos, 25:10 (2015), 15300–21  mathnet  crossref  isi
    17. A. V. Borisov, I. S. Mamaev, “Symmetries and reduction in nonholonomic mechanics”, Regul. Chaotic Dyn., 20:5 (2015), 553–604  mathnet  crossref
  • Нелинейная динамика
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