Integration of Hamiltonian systems on an isolated isoenergetic surface (Q810959)

In analytical dynamics, natural Hamiltonian systems, in particular, describing the motion of a rigid body in different fields of acting force, are integrable usually either on all isoenergetic surfaces or on none of them. The present paper proves the following theorem: There exists a class of 2-dimensional Hamiltonian systems which are non- integrable globally, but integrable on some particular 3-dimensional regular isoenergetic surface.