Grioli type precession of a heavy rigid body in a liquid (Q2761317)

The paper deals with the motion of a solid body bounded by a simply connected surface exposed to homogeneous gravitation field in infinite volume of ideal incompressible liquid. It is assumed that the liquid motion is irrotational and the liquid is resting at infinity. Besides, it is assumed that there is a flywheel in the body being of symmetrical form and rotating with a constant angular velocity with respect to an axis constantly connected with the body-carrier. Also, it is assumed that the weight of the liquid displaced by the body equals to the weight of the body with the flywheel. For such mechanical system, the conditions for the existence of solution are obtained. This solution corresponds to the class of motions for the case when the axis of body rotation and the body precession are not perpendicular.