The geometric phase and the dry friction of sleeping tops on inclined planes

We report on the motion of a spinning sleeping top an inclined plane. Below critical inclination angle tops are force free. The trajectory weakly planes in adiabatic limit is invariant angular frequency and thus under rescaling time, however not time reversal. stationary characterized by its Hannay type geometric to plane horizontal direction. At larger inclinations becomes unstable accelerates downhill. behavior points towards complex law dry friction contact point between tip material that depends slip parameter. propose phenomenological can explain relaxation into position, trajectories, instability at angles.