Geodesic
Geometrization of the Chaplygin reducing-multiplier theorem
Russian journal of nonlinear dynamics, Tome 9 (2013) no. 4, pp. 627-640

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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, reducing multiplier, Hamiltonization, conformally Hamiltonian system, Chaplygin ball.
Mots-clés : Poisson bracket, Poisson structure 
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     author = {A. V. Bolsinov and A. V. Borisov and I. S. Mamaev},
     title = {Geometrization of the {Chaplygin} reducing-multiplier theorem},
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A. V. Bolsinov; A. V. Borisov; I. S. Mamaev. Geometrization of the Chaplygin reducing-multiplier theorem. Russian journal of nonlinear dynamics, Tome 9 (2013) no. 4, pp. 627-640. http://geodesic.mathdoc.fr/item/ND_2013_9_4_a1/