A problem of libration with two degrees of freedom

Physics

Scientific paper

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Artificial Satellites, Geosynchronous Orbits, Librational Motion, Orbit Perturbation, Resonance, Circular Orbits, Degrees Of Freedom, Hamiltonian Functions, Harmonic Analysis

Scientific paper

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 momentum y1 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.

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