Abstract: The motion of a sphere＇ completely rolling in a freely moving sphere cavity on a smooth horizontal plane is investigated. The track equation of mass center of sphere and its any point on the edge of sphere in the inertial frame of reference are deduced, and their tracks are plotted. The period of tiny vibration of the sphere near the equilibrium position inside the sphere cavity is calculated, which is also compared with that of the sphere completely gliding inside a freely moving sphere cavity.

Key words: completely roll, kinetic track, period