INFLUENCE OF THE HYSTERESIS OF A COMPLIANT SUPPORT ON THE SPHERICAL MOTION OF A BODY CARRYING A FLYWHEEL

The motion of the axis of dynamic symmetry of a rigid body carrying a flywheel is investigated. The flywheel axis coincides with the body axis of symmetry. The system moves in the uniform gravitational field. The center of gravity of the system lies above the fixed point. The external viscous friction is taken into account. A radial compliant support resists the deviation of the axis of the body from the vertical. The support exhibits elastic and hysteretic properties. The reaction of this support is treated as an external force acting on the body. This force is represented as the sum of the linear elastic force and nonconservative force. The conditions of Lyapunov stability for the vertical orientation of the axis of the body are obtained in the linear approximation. As a result of the analysis of the periodic forced oscillations, three kinds of phasefrequency relations are identified. One of these relations has a point of minimum and a point of maximum. The theoretical results are confirmed by the experiment carried out with the rotor system of a separator which has a similar mechanical structure.