Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Department of Aeronautics and Astronautics

First Advisor

Christopher D. Hall, PhD


We apply noncanonical Hamiltonian methods to examine relative equilibria of a rigid body in a central gravitational field. These equilibria correspond to fixed points of a reduced set of equations expressed in a rotating frame and are representative of an orbiting satellite with fixed attitude relative to an observer rotating at the orbital rate. Our objective is to clarify the relationship between the classical approximation and a recent noncanonical Hamiltonian treatment. In contrast to the classical approximation, the orbital and attitude equations of motion for the noncanonical system remain coupled and the general solution is a circular orbit for which the orbit center and the center of attraction are not necessarily coincident. Our approach involves development of a hierarchy of Hamiltonian approximations. The hierarchy consists of the existing noncanonical system and two noncanonical formulations which we derive for rigid bodies subject to certain constraints motion about a fixed point and motion about a point following a Keplerian orbit. The classical solution is dynamically equivalent to this latter constrained (Keplerian) system. We apply Hamiltonian methods to identify relative equilibria and determine stability conditions. In general, we find that relative equilibria for the Keplerian and unconstrained systems are in close agreement.

AFIT Designator


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Astrodynamics Commons