Abstract:
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.
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The research of the first author was carried out in the framework of the state contract "Regular and Chaotic Dynamics" with Udmurt State University. The research of the second author was supported by grant no. 14-19-01303 of the Russian Science Foundation ("Dynamics and Control of Mobile Robototechnological Systems").
This publication is cited in the following 28 articles:
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