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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2013, Volume 9, Number 4, Pages 627–640
(Mi nd410)
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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.
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
Linking options:
https://www.mathnet.ru/eng/nd410 https://www.mathnet.ru/eng/nd/v9/i4/p627
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