David A. Ross

Date of Award

12-1991

Document Type

Thesis

Degree Name

Master of Science

Department

Department of Aeronautics and Astronautics

First Advisor

William E. Wiesel, PhD

Abstract

A perturbation theory for restricted three-body orbits, using a periodic trajectory as a reference solution, is investigated. The nearly- periodic equations of motions are derived by analogy to a linearization about an equilibrium point. In this case, the linearization produces a set of time- periodic equations of motion that, according to Floquet, are completely solved by a periodic trajectory. The four-dimensional phase space of the restricted three-body problem is the first surveyed for regions of periodic motion, via the surface of section phase plot. Upon extraction of a periodic orbit, nearly- periodic orbits are integrated. The integrated state vector is routinely sampled, and then twice transformed into a new set of variables. The first translates the frame center to the periodic trajectory. The second, or modal transformation, projects the coordinates along their eigenvectors. The transformations are highly useful, since two of the four new variables are constant within a finite region surrounding the periodic reference. Plots of the two variables are offered as an exact representation of a nearly-periodic trajectory, while plots of the constants over time, trace the boundaries of the nearly-periodic region.

AFIT Designator

AFIT-GA-ENY-91D-7

DTIC Accession Number

ADA243899

Comments

The author's Vita page is omitted.

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