Geodesic
Non-holonomic dynamics and Poisson geometry
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 69 (2014) no. 3, pp. 481-538 Cet article a éte moissonné depuis la source Math-Net.Ru

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This is a survey of basic facts presently known about non-linear Poisson structures in the analysis of integrable systems in non-holonomic mechanics. It is shown that by using the theory of Poisson deformations it is possible to reduce various non-holonomic systems to dynamical systems on well-understood phase spaces equipped with linear Lie–Poisson brackets. As a result, not only can different non-holonomic systems be compared, but also fairly advanced methods of Poisson geometry and topology can be used for investigating them. Bibliography: 95 titles.
Keywords: non-holonomic systems, Chaplygin ball, Suslov system, Veselova system.
Mots-clés : Poisson bracket 
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A. V. Borisov; I. S. Mamaev; A. V. Tsiganov. Non-holonomic dynamics and Poisson geometry. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 69 (2014) no. 3, pp. 481-538. http://geodesic.mathdoc.fr/item/RM_2014_69_3_a3/

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