Geodesic
On deformations of the canonical Poisson bracket for the nonholonomic Chaplygin and the Borisov--Mamaev--Fedorov systems on zero-level of the area integral.~I
Russian journal of nonlinear dynamics, Tome 7 (2011) no. 3, pp. 577-599

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We discuss the nonholonomic Chaplygin and the Borisov–Mamaev–Fedorov systems when the corresponding phase space is equivalent to cotangent bundle to dwo-dimensional sphere. In both cases Poisson bivectors are determined by $L$-tensors with non-zero torsion on the configurational space, in contrast with the well known Eisenhart–Benenti and Turiel constructions.
Keywords: nonholonomic mechanics, Chaplygin sphere
Mots-clés : Poisson brackets. 
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     author = {A. V. Tsiganov},
     title = {On deformations of the canonical {Poisson} bracket for the nonholonomic {Chaplygin} and the {Borisov--Mamaev--Fedorov} systems on zero-level of the area {integral.~I}},
     journal = {Russian journal of nonlinear dynamics},
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A. V. Tsiganov. On deformations of the canonical Poisson bracket for the nonholonomic Chaplygin and the Borisov--Mamaev--Fedorov systems on zero-level of the area integral.~I. Russian journal of nonlinear dynamics, Tome 7 (2011) no. 3, pp. 577-599. http://geodesic.mathdoc.fr/item/ND_2011_7_3_a12/