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Nelin. Dinam., 2010, Volume 6, Number 4, Pages 829–854 (Mi nd8)  

This article is cited in 12 scientific papers (total in 12 papers)

Hamiltonisation of non-holonomic systems in the neighborhood of invariant manifolds

A. V. Bolsinovab, A. V. Borisovc, I. S. Mamaevc

a M. V. Lomonosov Moscow State University
b School of Mathematics, Loughborough University
c Institute of Computer Science

Abstract: Hamiltonisation problem for non-holonomic systems, both integrable and non-integrable, is considered. This question is important for qualitative analysis of such systems and allows one to determine possible dynamical effects. The first part is devoted to the representation of integrable systems in a conformally Hamiltonian form. In the second part, the existence of a conformally Hamiltonian representation in a neighbourhood of a periodic solution is proved for an arbitrary measure preserving system (including integrable). General consructions are always illustrated by examples from non-holonomic mechanics.

Keywords: conformally Hamiltonian system, nonholonomic system, invariant measure, periodic trajectory, invariant torus, integrable system.

Full text: PDF file (398 kB)
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Document Type: Article
UDC: 517.925+517.938.5
MSC: 37Jxx
Received: 17.12.2010

Citation: A. V. Bolsinov, A. V. Borisov, I. S. Mamaev, “Hamiltonisation of non-holonomic systems in the neighborhood of invariant manifolds”, Nelin. Dinam., 6:4 (2010), 829–854

Citation in format AMSBIB
\Bibitem{BolBorMam10}
\by A.~V.~Bolsinov, A.~V.~Borisov, I.~S.~Mamaev
\paper Hamiltonisation of non-holonomic systems in the neighborhood of invariant manifolds
\jour Nelin. Dinam.
\yr 2010
\vol 6
\issue 4
\pages 829--854
\mathnet{http://mi.mathnet.ru/nd8}
\elib{http://elibrary.ru/item.asp?id=15574690}


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    This publication is cited in the following articles:
    1. A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Kachenie odnorodnogo shara po dinamicheski nesimmetrichnoi sfere”, Nelineinaya dinam., 6:4 (2010), 869–889  mathnet
    2. A. V. Bolsinov, A. V. Borisov, I. S. Mamaev, “Bifurkatsionnyi analiz i indeks Konli v mekhanike”, Nelineinaya dinam., 7:3 (2011), 649–681  mathnet
    3. A. V. Borisov, I. S. Mamaev, “Dinamika shara Chaplygina s polostyu, zapolnennoi zhidkostyu”, Nelineinaya dinam., 8:1 (2012), 103–111  mathnet
    4. 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
    5. Kozlov V.V., “Invariant Manifolds of Hamilton's Equations”, Pmm-J. Appl. Math. Mech., 76:4 (2012), 378–387  crossref  mathscinet  isi  elib  scopus
    6. 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
    7. A. V. Borisov, I. S. Mamaev, “Topologicheskii analiz odnoi integriruemoi sistemy, svyazannoi s kacheniem shara po sfere”, Nelineinaya dinam., 8:5 (2012), 957–975  mathnet
    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. A. V. Bolsinov, A. A. Kilin, A. O. Kazakov, “Topologicheskaya monodromiya v negolonomnykh sistemakh”, Nelineinaya dinam., 9:2 (2013), 203–227  mathnet
    10. 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
    11. Alexey V. Borisov, Ivan S. Mamaev, “The Dynamics of the Chaplygin Ball with a Fluid-filled Cavity”, Regul. Chaotic Dyn., 18:5 (2013), 490–496  mathnet  crossref  mathscinet  zmath
    12. A. V. Borisov, I. S. Mamaev, “Invariantnaya mera i gamiltonizatsiya negolonomnykh sistem”, Nelineinaya dinam., 10:3 (2014), 355–359  mathnet
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