Orbit propagation with Lie transfer maps in the perturbed Kepler problem
Healy, Liam M.
Celestial Mechanics and Dynamical Astronomy, Volume 85, Number 2, pp. 175-207, 2003.
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The Lie transfer map method may be applied to orbit propagation problems in celestial mechanics. This method, described in another paper, is a perturbation method applicable to Hamiltonian systems. In this paper, it is used to calculate orbits for zonal perturbations to the Kepler (two-body) problem, in both expansion in the eccentricity and closed form. In contrast with a normal form method like that of Deprit, the Lie transformations here are used to effect a propagation of phase space in time, and not to transform one Hamiltonian into another.