Luke J. Hagen

Date of Award


Document Type


Degree Name

Master of Science


Department of Aeronautics and Astronautics

First Advisor

William E. Wiesel, PhD.


The KAM Theory was developed in the 1960s but only in the last decade has it been applied to Earth orbiting satellites. Physical state variables of position and velocity are transformed into KAM Torus variables. The KAM Torus is a geometrical structure similar to that of a multi-dimensional donut. The Earth satellite's motion can be described as traversing the surface of this donut. There are two primary advantages of this transformation: (1) The new generalized coordinates which are analogous with mean anomaly, right ascension of the ascending node, and argument of perigee, increment linearly with time, and (2) Perturbations due to the Earth's geopotential are already embedded in a given torus to an arbitrary geopotential order. This study examines methods to describe perturbed satellite motion near a reference KAM Torus. The perturbations addressed in this thesis are atmospheric air drag and third-body effects from the Moon. Perturbed motion was integrated and compared against the unperturbed reference torus motion. For a sample orbit, expressions were numerically derived that allow the modification of the reference torus to allow prediction of the perturbed motion due to drag. It was shown that in the case of third-body lunar effects, the differences between perturbed motion and the reference torus motion cannot be generalized. Instead, there seems to be both evidence and motivation behind attempting to embed the lunar dynamics in the construction of Earth satellite KAM Tori.

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