A. James Clark School of Engineering

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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.
Paint by number: Uncovering phase flows of an integrable dynamical system
(American Institute of Physics, 1991-09) Healy, Liam; Deprit, Etienne
Given an integrable dynamical system with one degree of freedom, "painting" the integral over phase space proves to be a powerful technique for uncovering both global and local behavior. This graphical technique avoids numerical integration, employing instead a nonlinear method of assigning contrasting colors to the energy values to distinguish subtle details of the flow.