Aerospace Engineering Research Works

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

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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.
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.