On the motion of Chaplygin's sphere on a horizontal plane
The motion of Chaplygin's sphere, a heavy sphere on a fixed horizontal plane, is considered. It is assumed that the centre of mass of the sphere coincides with its geometric centre, and its principal central moments of inertia are different. In the unperturbed problem the sphere on an absolute smooth plane performs Euler-Poinsot motion about its centre, which moves rectilinearly and uniformly. In the case of low viscous or dry friction the perturbed motion of the sphere is investigated using the method of averaging. It is shown that the sphere tends to rotate about the axis of the largest principal central moment of inertia and the slip velocity approaches zero exponentially. In the case of dry friction and almost equal moments of inertia of the sphere, the system of averaged equations is fully integrable.
heavy sphere on a fixed horizontal plane
scientific article; zbMATH DE number 3928376