Steady and periodic modes in the problem of motion of a heavy material point on a rotating sphere (the viscous friction case)

The problem of motion of a heavy material point on a sphere uniformly rotating about a fixed axis is considered in the case of viscous friction. The angle of inclination between the axis and the horizon is constant. The existence, bifurcation, and stability of the equilibrium positions are discussed for such a mechanical system. The existence of periodic motions is also studied. An approach is proposed to find such motions in the case of low viscosity.