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