Integrable cases in the problem on a heavy cylindrical body falling within a liquid (Q1584123)

The paper deals with the motion equations for a heavy solid in an ideal liquid in the presence of circulation in the form of Kirchhoff equations [see \textit{V.~V.~Kozlov}, Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela 1993, No.~4, 113--117 (1993)]. The author obtains explicit formulas for solution of the equations in the case of dynamical symmetry. In the case of the inertial motion of the body (the body weight equals to zero) the boundedness of the body motion trajectory is proved.