Aerospace Engineering Research Works

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

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Author: search.filters.author.Healy, LiamSubject: search.filters.subject.Hamiltonian system

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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.
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    The Phase Space Portrait of an Integrable Dynamical System
    (Science, 1990-02-16) Coffey, Shannon; Deprit, André; Deprit, Etienne; Healy, Liam
    For an integrable dynamical system with one degree of freedom, "painting" the integral over the phase space proves to be very effective for uncovering the global flow down to minute details. Applied to the main problem in artificial satellite theory, for instance, the technique reveals an intricate configuration of equilibria and bifurcations when the polar component of the angular momentum approaches zero.