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Orbit Propagation with Lie Transfer Maps in the Perturbed Kepler Problem

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Abstract

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.

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  1. Naval Research Laboratory, Code 8233, Washington, DC, 20375-5355, U.S.A., e-mail

    Liam M. Healy

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  1. Liam M. Healy
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Healy, L.M. Orbit Propagation with Lie Transfer Maps in the Perturbed Kepler Problem. Celestial Mechanics and Dynamical Astronomy 85, 175–207 (2003). https://doi.org/10.1023/A:1022055721875

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  • DOI: https://doi.org/10.1023/A:1022055721875

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