A problem of libration with two degrees of freedom

Moore (1983) presented a theory of resonance with two degrees of freedom based on the Bohlin-von Zeipel procedure. This procedure is now applied to librational motion with all constants re-evaluated in terms of values of the momenta given either by the initial conditions, or, in the case of the momentumy₁ conjugate to the critical argument x₁, by its value at the libration centre. Numerical results are presented for a resonant satellite in a near 12 hr orbit and for a geosynchronous satellite. The theory is further developed to include near-circular orbits by recasting the problem in terms of the Poincaré eccentric variables.