Geodesic
On the Nonlinear Poisson Bracket Arising in Nonholonomic Mechanics
Matematičeskie zametki, Tome 95 (2014) no. 3, pp. 340-349

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Nonholonomic systems describing the rolling of a rigid body on a plane and their relationship with various Poisson structures are considered. The notion of generalized conformally Hamiltonian representation of dynamical systems is introduced. In contrast to linear Poisson structures defined by Lie algebras and used in rigid-body dynamics, the Poisson structures of nonholonomic systems turn out to be nonlinear.
Mots-clés : Poisson bracket, Poisson structure
Keywords: nonholonomic system, dynamical system, conformally Hamiltonian representation, Casimir function, Routh sphere, rolling of a Chaplygin ball. 
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     author = {A. V. Borisov and I. S. Mamaev and A. V. Tsiganov},
     title = {On the {Nonlinear} {Poisson} {Bracket} {Arising} in {Nonholonomic} {Mechanics}},
     journal = {Matemati\v{c}eskie zametki},
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A. V. Borisov; I. S. Mamaev; A. V. Tsiganov. On the Nonlinear Poisson Bracket Arising in Nonholonomic Mechanics. Matematičeskie zametki, Tome 95 (2014) no. 3, pp. 340-349. http://geodesic.mathdoc.fr/item/MZM_2014_95_3_a2/