Bifurcations of the relative equilibria of a heavy bead on a hoop uniformly rotating about an inclined axis with dry friction

The sliding of a heavy bead threaded onto a thin circular hoop rotating at a constant angular velocity about an inclined axis located in its plane and passing through its centre is considered. A dry friction force acts between the bead and the hoop. The sets of the non-isolated positions of relative equilibrium of the bead on the hoop are found and their dependence on the parameters of the problem is investigated. The results are presented in the form of bifurcation diagrams.