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Mat. Sb., 2016, Volume 207, Number 7, Pages 3–28 (Mi msb8552)  

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

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.

DOI: https://doi.org/10.4213/sm8552

Full text: PDF file (620 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2016, 207:7, 889–914

Bibliographic databases:

UDC: 517.927.71+517.927.75
PACS: 45.40.Cc
MSC: Primary 70E15; Secondary 70E20, 70E40, 70E50
Received: 31.05.2015 and 05.04.2016

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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