The Titan-Hyperion orbital resonance

Abstract

Considerable effort was spent investigating the applicability of a Hamiltonian averaged over high frequency terms, where long period and secular terms up to second order in eccentricity were kept. The Hamiltonian that is given from the planar, elliptic, restricted three body problem applied to Titan-Hyperion, when the Kepler terms are also expanded to second order in small quantities and several conical transformations are carried out, is presented and discussed.