Abstract
A coordinate system is defined on the phase space of a perturbed Keplerian system after the mean anomaly has been averaged out, for the purpose of explaining how eliminating the longitude of the ascending node reduces the orbital space to a two-dimensional sphere in case the system admits an axial symmetry. Concomitantly, on the submanifold of direct osculating ellipses, the CDM variables are replaced by functions which form the basis of a Poisson algebra isomorphic to the Lie algebra so(3) of the rotation group SO(3); furthermore, in these variables, the doubly reduced phase flow appears like a rotation of the reduced phase space.
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References
Coffey, S. L., Deprit, A., and Miller, B. R.: 1986, Celest. Mech., 39, 365–406.
Cushman, R.: 1983, Celest. Mech., 31, 401–429.
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Ferrer, S., Miller, B.R. Coordinates for perturbed keplerian systems with axial symmetry. Celestial Mech Dyn Astr 53, 3–10 (1992). https://doi.org/10.1007/BF00049358
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DOI: https://doi.org/10.1007/BF00049358