Transgression Effect in the Problem of the Rolling of a Ball in a Recess

In this paper, the problem of the rolling of a heavy ball (a rigid body bounded by the surface of a sphere, such that its center of mass coincides with the center of sphere while all the principal central moments of inertia are equal to each other) without slipping on a convex surface in the vicinity of its lower point of elliptical type is considered. The evolution of the angular velocity component of the ball in the projection onto the vertical direction is described.