Geodesic
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
Sbornik. Mathematics, Tome 207 (2016) no. 7, pp. 889-914

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
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     author = {A. V. Belyaev},
     title = {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},
     journal = {Sbornik. Mathematics},
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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. Sbornik. Mathematics, Tome 207 (2016) no. 7, pp. 889-914. http://geodesic.mathdoc.fr/item/SM_2016_207_7_a0/