On Analogs of the Bobylev–Steklov Case for a Gyrostat under the Action of a Moment of Gyroscopic Forces

Equations of motion of a gyrostat around a fixed point under the action of a moment of gyroscopic forces are studied. Analogs of the Bobylev–Steklov case are obtained; it is shown that, unlike the classical case of a rigid body, Bobylev’s and Steklov’s approaches are not equivalent and can provide complementary results. Conditions have been found under which parametric families of particular solutions expressed in terms of elliptic functions can be constructed. Six types of stationary solutions are singled out, and the conditions for their stability are obtained using the method of the Chetayev integral connections.