  We consider the motion of a particle on a surface which is a small
perturbation of the standard sphere. One may qualitatively describe the motion
by means of a precessing great circle of the sphere. The observation is
employed to derive a subsidiary Hamiltonian system that has the form of
equations for the top with a 4-th order Hamiltonian, and provides the detailed
asymptotic description of the particle's motion in terms of graphs on the
standard sphere.
