On Solutions of the Equations of Motion of a Gyrostat with a Variable Gyrostatic Moment

The problem of the motion of a gyrostat with a variable gyrostatic moment under the action of potential and gyroscopic forces is considered. Three new solutions of the equations of motion are obtained, which are determined by three linear invariant relations for the components of the angular velocity vector of the gyrostat. In the case of a heavy gyrostat, a solution is found when the gyrostat mass distribution is characterized by the Kovalevskaya and Goryachev-Chaplygin generalized conditions. The next two solutions are valid for equations of the Kirchhoff-Poisson class. One of them exists in the case of dynamically symmetric gyrostats, and in the other solution the gyrostat mass distribution is arbitrary.