On the integrability and stability of stationary solutions of the Goryachev—Sretensky gyrostat

The equations of motion of the Goryachev-Sretensky gyrostat are studied. All stationary solutions are found on the invariant set of the zero level of the area integral and their stability is analyzed. For the case where the suspension point coincides with the center of mass and the action of a gyroscopic moment of a special type, integration in quadratures is performed.