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This article is cited in 1 scientific paper (total in 1 paper)
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.
Received: 18.03.2019 Accepted: 30.04.2019
Citation:
Ivan Yu. Polekhin, “Precession of the Kovalevskaya and Goryachev – Chaplygin Tops”, Regul. Chaotic Dyn., 24:3 (2019), 281–297
Linking options:
https://www.mathnet.ru/eng/rcd478 https://www.mathnet.ru/eng/rcd/v24/i3/p281
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Abstract page: | 203 | References: | 42 |
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