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Nelin. Dinam., 2013, Volume 9, Number 4, Pages 627–640 (Mi nd410)  

This article is cited in 3 scientific papers (total in 3 papers)

Geometrization of the Chaplygin reducing-multiplier theorem

A. V. Bolsinovab, A. V. Borisovcad, I. S. Mamaevacd

a Laboratory of nonlinear analysis and the design of new types of vehicles, Institute of Computer Science, Udmurt State University, Universitetskaya 1, Izhevsk, 426034 Russia
b School of Mathematics, Loughborough University, United Kingdom, LE11 3TU, Loughborough, Leicestershire
c A. A. Blagonravov Mechanical Engineering Institute of RAS, Bardina str. 4, Moscow, 117334, Russia
d Institute of Mathematics and Mechanics of the Ural Branch of RAS, S. Kovalevskaja str. 16, Ekaterinburg, 620990, Russia

Abstract: This paper develops the theory of the reducing multiplier for a special class of nonholonomic dynamical systems, when the resulting nonlinear Poisson structure is reduced to the Lie–Poisson bracket of the algebra $e(3)$. As an illustration, the Chaplygin ball rolling problem and the Veselova system are considered. In addition, an integrable gyrostatic generalization of the Veselova system is obtained.

Keywords: nonholonomic dynamical system, Poisson bracket, Poisson structure, reducing multiplier, Hamiltonization, conformally Hamiltonian system, Chaplygin ball.

Full text: PDF file (298 kB)
References: PDF file   HTML file

Document Type: Article
UDC: 531.8, 517.925
MSC: 37J60, 37J35, 70E18, 53D17
Received: 19.09.2012
Revised: 22.11.2012

Citation: A. V. Bolsinov, A. V. Borisov, I. S. Mamaev, “Geometrization of the Chaplygin reducing-multiplier theorem”, Nelin. Dinam., 9:4 (2013), 627–640

Citation in format AMSBIB
\Bibitem{BolBorMam13}
\by A.~V.~Bolsinov, A.~V.~Borisov, I.~S.~Mamaev
\paper Geometrization of the Chaplygin reducing-multiplier theorem
\jour Nelin. Dinam.
\yr 2013
\vol 9
\issue 4
\pages 627--640
\mathnet{http://mi.mathnet.ru/nd410}


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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. Borisov, I. S. Mamaev, A. V. Tsiganov, “Non-holonomic dynamics and Poisson geometry”, Russian Math. Surveys, 69:3 (2014), 481–538  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “Superintegrable Generalizations of the Kepler and Hook Problems”, Regul. Chaotic Dyn., 19:3 (2014), 415–434  mathnet  crossref  mathscinet  zmath
    3. I. A. Bizyaev, V. V. Kozlov, “Homogeneous systems with quadratic integrals, Lie-Poisson quasibrackets, and Kovalevskaya's method”, Sb. Math., 206:12 (2015), 1682–1706  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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