| Abstract: | The motion of a heavy sphere on a fixed horizontal plane is considered. It is assumed that the centre of mass of the sphere is at its geometric centre, while the principal central moments are different (Chaplygin's sphere). Using the method of averaging, the motion of the sphere is investigated under slip conditions when there is low viscous and also low dry friction. It is shown that when the sphere moves with viscous friction it tends, for the majority of initial data, to rotate about the longest of the axes of the principal central moments of inertia. The motion of the sphere centre tends to become uniform so that the slip velocity approaches zero exponentially. A system of averaged equations, which is fully integrable, is obtained in the case of almost equal moments of inertia, when the friction is dry. The solutions are analyzed. |
