On a new particular solution of the equations of motion of a heavy solid in a liquid (Q1086064)

The Kirchhoff-Clebsch equations of motion of a free heavy solid in a fluid are considered under Chaplygin conditions. The precession motions of a solid are investigated in which the rotating part consists of two rotary motions, the direction of rotation of the first is constant in space, and the second is constant in the solid, the angle between the two being constant. Means for finding precession motions of the solid in fluid are indicated. A particular solution is given for the case when the angular velocity components of the rotary motions are equal and the direction of their rotation mutually perpendicular. This solution is similar to that of Grioli problem of the motion of a heavy solid with a single fixed point. The geometric interpretation of a solid in fluid, defined by that solution is given.