The Dynamics of a Ball Rolling on a Rotating Plane

In the absence of any viscous or rolling resistance, a ball set on a uniformly rotating horizontal plane does not leave the plane but moves in a circular orbit. The equations of motion, when both viscous drag and rolling resistance are present, were set up by Fufaev [1] and Abdelkader [2] obtained a complicated implicit solution of the equations. In this paper we show that solutions may be found explicitly. The solutions depend on two parameters which determine whether the ball spirals towards, or away from, the axis of rotation, onto a circular orbit, or onto a fixed point.