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Tr. Mat. Inst. Steklova, 2016, Volume 295, Pages 41–52 (Mi tm3746)  

Generalizations of the Kovalevskaya case and quaternions

I. A. Bizyaev, A. V. Borisov, I. S. Mamaev

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

Abstract: This paper provides a detailed description of various reduction schemes in rigid body dynamics. The analysis of one of such nontrivial reductions makes it possible to put the cases already found in order and to obtain new generalizations of the Kovalevskaya case to $e(3)$. Note that the indicated reduction allows one to obtain in a natural way some singular additive terms that were proposed earlier by D. N. Goryachev.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.1134/S0371968516040038

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English version:
Proceedings of the Steklov Institute of Mathematics, 2016, 295, 33–44

Bibliographic databases:

Document Type: Article
UDC: 531.381
Received: July 6, 2016

Citation: I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Generalizations of the Kovalevskaya case and quaternions”, Modern problems of mechanics, Collected papers, Tr. Mat. Inst. Steklova, 295, MAIK Nauka/Interperiodica, Moscow, 2016, 41–52; Proc. Steklov Inst. Math., 295 (2016), 33–44

Citation in format AMSBIB
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\pages 41--52
\publ MAIK Nauka/Interperiodica
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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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