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This article is cited in 6 scientific papers (total in 6 papers)
A topological classification of the Chaplygin systems in the dynamics of a rigid body in a fluid
S. S. Nikolaenko M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract:
The paper is concerned with the topological analysis of the Chaplygin integrable case in the dynamics of a rigid body in a fluid. A full list of the topological types of Chaplygin systems in their dependence on the energy level is compiled on the basis of the Fomenko-Zieschang theory. An effective description of the topology of the Liouville foliation in terms of natural coordinate variables is also presented, which opens a direct way to calculating topological invariants. It turns out that on all nonsingular energy levels Chaplygin systems are
Liouville equivalent to the well-known Euler case in the dynamics of a rigid body with fixed point.
Bibliography: 23 titles.
Keywords:
Kirchhoff's equations, Chaplygin case, integrable Hamiltonian system, Liouville foliation, Fomenko-Zieschang invariant.
Received: 04.06.2013
Citation:
S. S. Nikolaenko, “A topological classification of the Chaplygin systems in the dynamics of a rigid body in a fluid”, Mat. Sb., 205:2 (2014), 75–122; Sb. Math., 205:2 (2014), 224–268
Linking options:
https://www.mathnet.ru/eng/sm8251https://doi.org/10.1070/SM2014v205n02ABEH004373 https://www.mathnet.ru/eng/sm/v205/i2/p75
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Abstract page: | 532 | Russian version PDF: | 208 | English version PDF: | 26 | References: | 88 | First page: | 46 |
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