Bifurcations of the relative equilibria of a heavy bead on a rotating hoop with dry friction

The sliding of a heavy bead, threaded on a thin circular hoop, rotating with a constant angular velocity around a vertical axis, situated in its plane and, in the general case, not passing through its vertical diameter, is considered. It is assumed that dry friction acts between the bead and the hoop. A set of unisolated positions of relative equilibrium of the bead on the hoop is obtained, and their dependence on the problem parameters is investigated. The results are presented in the form of bifurcation diagrams. The stability properties of the unisolated relative equilibria obtained are discussed.