Topological analysis of classical integrable systems in the dynamics of the rigid body

Details Topological analysis of classical integrable systems in the dynamics of the rigid body Topological analysis of classical integrable systems in the dynamics of the rigid body

2009-06-14

arxiv.org/abs/0906.2548v2

Soviet Mathematics-Doklady, 1983, Vol. 28, No. 3, pp. 802-805

Nonlinear Sciences

Exactly Solvable and Integrable Systems

LaTex, 4 pages, 4 figures

Scientific paper

The general integrability cases in the rigid-body dynamics are the solutions of Lagrange, Euler, Kovalevskaya, and Goryachev-Chaplygin. The first two can be included in Smale's scheme for studying the phase topology of natural systems with symmetries. We modify Smale's program to suit the most complicated last two cases with non-linear first integrals. The bifurcation sets are found and all transformations of the integral tori are described and classified. New non-trivial bifurcation of a torus is established in the Kovalevskaya and Goraychev-Chaplygin cases.

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