Movement of a ball colliding rough surface / T. F. Barbashova, L. S. Otradnova. //Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2012. № 5. P. 35-39 [Moscow Univ. Math. Bulletin. Vol. 67, N 5, 2012.].
Some problems of sphere's movement by inertia, such as the movement between two parallel planes, inside a sphere and inside a circular cylinder are considered. We assume that during the impact the condition of rolling without slipping is satisfied (a nonholonomic constraint): the tangent velocity of a contacting sphere's point is equal to zero. It is shown that in all cases the movement tends in a limit to a stable velocity mode: the angular sphere's velocity tends to a constant value and its center velocity becomes periodic for planes and conditionally periodic for the sphere and the cylinder. In some cases the coordinates specifying the sphere's position and orientation come to a stable mode.
Key words: {sphere's movement by inertia, impacts, rolling without slipping, nonholonomic constraints.}