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.
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    The Main Problem in Satellite Theory Revisited
    (Springer Science+Business Media B.V., 2000) Healy, Liam M.
    Abstract. Using the elimination of the parallax followed by the Delaunay normalization, we present a procedure for calculating a normal form of the main problem (J2 perturbation only) in satellite theory. This procedure is outlined in such a way that an object-oriented automatic symbolic manipulator based on a hierarchy of algebras can perform this computation. The Hamiltonian after the Delaunay normalization is presented to order six explicitly in closed form, that is, in which there is no expansion in the eccentricity. The corresponding generating function and transformation of coordinates, too lengthy to present here to the same order; the generator is given through order four.
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    Computation of error effects in nonlinear Hamiltonian systems using Lie algebraic methods
    (American Institute of Physics, 1992-06) Healy, Liam; Dragt, Alex; Gjaja, Ivan
    There exist Lie algebraic methods for obtaining transfer maps around any given trajectory of a Hamiltonian system. This paper describes an iterative procedure for finding transfer maps around the same trajectory when the Hamiltonian is perturbed by small linear terms. Such terms often result when an actual system deviates from an ideal one due to errors. Two examples from accelerator physics are worked out. Comparisons with numerical computations, and in simple cases exact analytical calculations, demonstrate the validity of the procedure.