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 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.
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