Aerospace Engineering Research Works

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

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End date: 2024Subject: search.filters.subject.computer algebra

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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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    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.
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    Symbolic and Parallel Computation in Celestial Mechanics
    (Society for Industrial and Applied Mathematics, 1996) Healy, Liam
    One aspect of celestial mechanics is the computation of the long-term orbits of celestial bodies. This type of computation is complicated by the interaction of the many bodies that need to be considered to derive accurate long-term behavior. For reasons explained in this chapter, it is necessary to do this symbolically rather than numerically. Symbolic computations performed on a Lisp machine are described. The visualization of the solution is accomplished in a massively parallel SIMD machine.
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    A Toolbox for Nonlinear Dynamics
    (Springer-Verlag, 1991) Coffey, Shannon; Deprit, André; Deprit, Eitenne; Healy, Liam; Miller, Bruce
    Using the main problem of artificial satellite theory as an illustration, we review several developments which have had a significant impact on research in nonlinear dynamics. On the mathematical front, we point to the theory of Lie transformations; in the area of computational software, we explain how massively data parallel machines open the way for symbolic solution of large problems. Finally, we show how color graphics assist in the qualitative analysis of dynamical systems.