A topological classification of the Chaplygin systems in the dynamics of a rigid body in a fluid

S. S. Nikolaenko

Sbornik. Mathematics, Tome 205 (2014) no. 2, pp. 224-268

Résumé

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.

Détail

Keywords: Kirchhoff's equations, Chaplygin case, integrable Hamiltonian system
Mots-clés : Liouville foliation, Fomenko-Zieschang invariant.

Bibliographie

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