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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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