  We compute the normal forms for the Hamiltonian leading to the epicyclic
approximations of the (perturbed) Kepler problem in the plane. The Hamiltonian
setting corresponds to the dynamics in the Hill synodic system where, by means
of the tidal expansion of the potential, the equations of motion take the form
of perturbed harmonic oscillators in a rotating frame. In the unperturbed,
purely Keplerian case, the post-epicyclic solutions produced with the normal
form coincide with those obtained from the expansion of the solution of the
Kepler equation. In all cases where the perturbed problem can be cast in
autonomous form, the solution is easily obtained as a perturbation series. The
generalization to the spatial problem and/or the non-autonomous case is
straightforward.
