Abstract
The equations of motion of the Goryachev–Sretensky gyrostat are studied. It has been established that one component of the angular velocity vector oscillates with zero average value on all solutions outside the set of zero level of the area integral. All stationary solutions are found, including two states of rest and two parametric families of permanent rotations. Using Chetaev’s method of integral connectives, sufficient conditions for the stability of stationary solutions are obtained. Based on the analysis of the roots of the characteristic equation, instability conditions were obtained. The possibility of gyroscopic stabilization due to the moment of circular-gyroscopic forces under certain conditions has been established.
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