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Precession of the Kovalevskaya and Goryachev-Chaplygin tops. (English) Zbl 1428.70013
Summary: The change of the precession angle is studied analytically and numerically for two classical integrable tops: the Kovalevskaya top and the Goryachev-Chaplygin top. Based on the known results on the topology of Liouville foliations for these systems, we find initial conditions for which the average change of the precession angle is zero or can be estimated asymptotically. Some more difficult cases are studied numerically. In particular, we show that the average change of the precession angle for the Kovalevskaya top can be non-zero even in the case of zero area integral.
MSC:
70E17 Motion of a rigid body with a fixed point
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
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