Ideal Resonance Problem: the Post-Post-Pendulum Approximation

Abstract

Explicit construction of the solutions of the Hamiltonian system given by H = H0(J) − e A(J) cos Θ (ideal resonance problem), two orders of approximation beyond the well-known pendulum approximation. The given solutions are valid for libration amplitudes of order \(\mathcal{O}\left( {\sqrt[4]{\varepsilon }} \right)\). The procedure used is extended to allow the construction of the solutions of Hamiltonians with perturbations involving two degrees of freedom; the post-pendulum solution of an example of this kind is constructed.