The Ideal Resonance Problem: A comparison of the solutions expressed in terms of mean elements and in terms of initial conditions

Abstract

In an earlier publication (Jupp, 1972), a solution of the Ideal Resonance Problem is exhibited explicitly in terms of the ‘mean’ elements; to second order in the small parameter in the case of libration, and to first order in the case of deep circulation. Both representations possess a singularity when the ‘mean’ modulus of the Jacobi elliptic functions is unity; this corresponds to the separatrix of the phase plane of the dynamical system.