Stability of the motion of the system 'rotating disk - flexible rod'

Equations are presented which describe the perturbed motion of a system consisting of a rotating disk coupled via a cylindrical hinge with a flexible rod whose lower end is clamped. These equations are then used to analyze the stability of the main form of motion whereby the rod remains in a vertical position while the disk rotates in the horizontal plane. It is shown that the onset of instability may occur when, for a given angular velocity, the gravity force of the disk is equal to the Euler force. If the disk gravity force is less than the Euler force, the system is unstable at any angular velocity.