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A problem of libration with two degrees of freedom

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Abstract

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 momentumy 1 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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Authors and Affiliations

  1. Earth Satellite Research Unit, Department of Mathematics, University of Aston in Birmingham, Birmingham, UK

    P. Moore

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  1. P. Moore
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Moore, P. A problem of libration with two degrees of freedom. Celestial Mechanics 33, 49–69 (1984). https://doi.org/10.1007/BF01231094

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  • DOI: https://doi.org/10.1007/BF01231094

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