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 Hannay type geometric 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.

我们报告了在倾斜平面上旋转的睡顶的运动。低于临界倾角时，睡上衣不受力。在绝热极限的弱倾斜平面上的睡眠陀螺的轨迹是陀螺角频率不变的，因此在时间重新标度下是不变的，但在时间反转时不是不变的。睡顶的静止轨迹的特征在于其与平面内水平方向的汉内型几何角度。在平面的较大倾斜度下，顶部的静止运动变得不稳定并且顶部加速下坡。该行为指向顶部尖端与斜面材料之间接触点的复杂干摩擦定律，该定律取决于滑动参数。