On two classes of precession motions of a gyrostat under the action of potential and gyroscopic forces

We find two new classes of precession motions of a gyrostat with fixed point. The motions are described by the Kirchhoff differential equations. For the first class, the velocities of precession and free rotation are equal and given in the form of a trigonometric polynomial of the first degree in the angle of free rotation. For the second class, the precession and rotation velocities do not coincide and are defined by special functions of the angle of free rotation. These classes are described in terms of new solutions of the Kirchhoff equations.