Stability of a stationary rotation of rigid body hanged on a ``short'' string (Q2754832)

The following mechanical system is considered: a heavy cylinder is hanged on absolutely flexible, inextensible string which rotates with angular velocity \(\omega \) about vertical axis. The authors examine stability of the stationary rotations which is characterized by the following conditions: the system rotates as a single unit and the cylinder is situated between the vertical axis and the string axis. To obtain stability conditions of such a motion, the authors analyze the cubic characteristic equation of the linearized system by means of the graph-analytic method. Stability zones in the plane of two parameters \(e\) and \(\theta^0\) are constructed. Here \(e=r^2/a^2\), \(r\) is the radius of cylinder, \(2a\) is the height of the cylinder, and \(\theta^0\) is the angle between the string and the vertical axis.