Transgression Effect in the Problem of the Motion of a Rod on a Cylinder

The motion of a heavy rigid thin rod on the surface of a right circular cylinder is considered. It is assumed that the angle between the generatrix of the cylinder and the direction of gravity is nonzero. The positions of equilibria of the rod on a cylinder form an equilibrium manifold (for all these equilibria the rod rests on the cylinder by its center of mass). The effect of transgression (nontrivial evolution along the equilibrium manifold) of the rod on the cylinder is studied using the normal form method.