Global attraction of steady motions of a gimbal-mounted asynchronous gyroscope

The subject of consideration is a gyroscope mounted in the gimbal (Cardan) suspension and placed on the immovable foundation in the field of gravity. Dissipative and control torques on the axes of gimbals are supposed to be absent, but the fast rotating rotor is under the action of the frictional torque, and so the device is supplied with the asynchronous electric motor that forms a driving torque acting about the axis of rotation of the rotor in the inner gimbal. The inner gimbal serves as the stator of the motor. This device has a family of steady motions, which are steady precessions of the rotor about the outer gimbal axis and steady rotations of the rotor about its axis of rotation in the inner gimbal. In the paper, the global attraction property is proved for the set of steady motions. This means that every motion of the device tends to one of its steady motions as time tends to infinity. Outcomes of numerical simulation are presented to give a demonstration of this property.