The transgression effect in the problem of a ball rolling in a hole

We consider the problem of rolling without sliding a heavy ball (a rigid body bounded by the surface of a sphere and such that its center of mass coincides with the center of the sphere, and all the principal central moments of inertia are equal to each other) along the convex surface in the vicinity of its lower point of elliptical type. The evolution of the angular velocity of the ball in projection onto the vertical (the transgression effect) is described.