Transgression effect in the problem of motion of a rod on a cylinder

The problem of motion of a heavy rigid thin rod on a perfectly rough right circular cylinder is considered. It is assumed that the generatrix of the cylinder has a nonzero angle with the direction of gravity. The equilibrium positions of the rod on a cylinder form the equilibria manifold (for all these equilibria the rod touches the cylinder by its center of mass). The effect of transgression (nontrivial evolution along the equilibria manifold) of the rod on the cylinder is studied by the normal form method.