On Rolling of a Heavy Disk on a Surface of Revolution with Negative Curvature

Abstract

In the problem on rolling of a heavy round homogeneous disk on a surface of revolution with a negative Gaussian curvature, the classical nonholonomic model is used in which, at each moment, the instantaneous velocity of the current drive point of the disk touching the support is zero. Stationary motions of the disk are found. We note that, within the nonholonomic model the tangential component of the reacton for a stationary motion can be larger than the pressure force. This means that such motion in practice cannot be implemented or observed if we assume that the force that provides the no-slip condition is the dry friction force with a coefficient between zero and unity. For stationary motions of the disk the conditions of the stability in the first approximation are obtained. The results of the numerical simulation of the rolling motion of the disk without slip while the mechanical energy dissipation occurs, are presented. The purpose of these studies was to verify the adequacy of the assumed nonholonomic model of coin movements observed in practice in the entertaining coinboxes of the plastic funnel type.