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Regul. Chaotic Dyn., 2019, Volume 24, Issue 3, Pages 281–297 (Mi rcd478)  

Precession of the Kovalevskaya and Goryachev Chaplygin Tops

Ivan Yu. Polekhin

Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: 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.

Keywords: mean motion, Kovalevskaya top, Goryachev Chaplygin top, integrable system, precession

Funding Agency Grant Number
Russian Science Foundation 19-71-30012
This research was funded by a grant from the Russian Science Foundation (Project No. 19-71-30012).


References: PDF file   HTML file
MSC: 70E17, 37J35
Received: 18.03.2019
Accepted:30.04.2019
Language:

Citation: Ivan Yu. Polekhin, “Precession of the Kovalevskaya and Goryachev Chaplygin Tops”, Regul. Chaotic Dyn., 24:3 (2019), 281–297

Citation in format AMSBIB
\Bibitem{Pol19}
\by Ivan Yu. Polekhin
\paper Precession of the Kovalevskaya and Goryachev Chaplygin Tops
\jour Regul. Chaotic Dyn.
\yr 2019
\vol 24
\issue 3
\pages 281--297
\mathnet{http://mi.mathnet.ru/rcd478}


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