On the Motion of a Bead on a Rough Hoop Freely Rotating Around a Vertical Diameter

We consider the problem of the motion of a heavy bead strung on a rough heavy hoop freely rotating around a vertical diameter. Non-isolated sets of steady motions of the system are identified, and their bifurcation diagrams are constructed. The dependence of these solutions on an essential parameter of the problem—the constant of the cyclic integral—is studied. The results obtained are compared with the results obtained previously for the case when a rough hoop rotates around a vertical diameter with a constant angular velocity. Typical phase portraits are constructed for various combinations of system parameters.