Hamiltonian equations of the planetary N-body problem in the post-Newtonian approximation

The canonical equations in the planetary problem of N bodies having a spherical symmetry in the post-Newtonian approximation of the general relativity theory are obtained. It is ascertained that the influence of the rotational motion of planets in the solar system on the translational one has the same order as the primary components of relativistic effects. The influence of the post-Newtonian term in the Hamiltonian function on the secular changes of the orbital elements is considered. The relativistic correction is shown to have a value and an analytical structure such that it is possible to apply the KAM theory conclusions on the existence of nearly-periodic solutions of the planetary N-body problem quite as much in the post-Newtonian case as in the classical one.