Aerospace Engineering Research Works

Permanent URI for this collectionhttp://hdl.handle.net/1903/1655

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Orbit propagation with Lie transfer maps in the perturbed Kepler problem
(Springer Science+Business Media B.V., 2003-02) Healy, Liam M.
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.
Automatic Rendering of Astrodynamics Expressions for Efficient Evaluation
(American Astronautical Society, 1998) Healy, Liam M.; Travisano, Jeffrey J.
In this paper, we describe the automatic rendering of expressions computed using symbolic manipulation. Computations from astrodynamics frequently can be put in a fixed hierarchy of polynomials and Fourier series. Once in this form, FORTRAN subprograms can be generated automatically in a form that lends itself to numerical evaluation. The goal of the current work is to present an approach for using symbolic manipulation techniques to produce a Fortran representation of the normalized Hamiltonian and other supporting equations representing as many of the actual physical effects on satellites as possible.