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Sbornik: Mathematics, 2016, Volume 207, Issue 7, Pages 889–914
DOI: https://doi.org/10.1070/SM8552 (Mi sm8552) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Representation of solutions to the problem of the motion of a heavy rigid body in the Kovalevskaya case in terms of Weierstrass $\zeta$- and $\wp$-functions and nonintegrability of the Hess case by quadratures

A. V. Belyaev

Novosibirsk State University
English version PDF (583 kB) Citations (3)
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DOI: https://doi.org/10.1070/SM8552
Abstract: A method for the representation of Delaunay's solutions and some other particular solutions to the problem of the motion of a heavy rigid body in the Kovalevskaya case in terms of the Weierstrass $\zeta$- and $\wp$-functions is put forward. The Hess case in the problem of the motion of a heavy rigid body is shown to be nonintegrable by quadratures.
Bibliography: 24 titles.
Keywords: Kovalevskaya case, Hess case, complete integrability, asymptotic behaviour of solutions, singular points of solutions.
Received: 31.05.2015 and 05.04.2016
Russian version:
Matematicheskii Sbornik, 2016, Volume 207, Number 7, Pages 3–28
DOI: https://doi.org/10.4213/sm8552
Bibliographic databases:
Document Type: Article
UDC: 517.927.71+517.927.75
PACS: 45.40.Cc
MSC: Primary 70E15; Secondary 70E20, 70E40, 70E50
Language: English
Original paper language: Russian
Citation: A. V. Belyaev, “Representation of solutions to the problem of the motion of a heavy rigid body in the Kovalevskaya case in terms of Weierstrass $\zeta$- and $\wp$-functions and nonintegrability of the Hess case by quadratures”, Mat. Sb., 207:7 (2016), 3–28; Sb. Math., 207:7 (2016), 889–914
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:63
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