Angles measurements from optical systems are the primary source of data for maintaining the orbits of high altitude satellites. Radar measurements are used primarily for low Earth orbit (LEO) satellites. Recently it has been shown that the accuracy of the orbit updates using only optical system angles-only data is just as good, if not better, than the performance from radar systems for LEO satellites. The purpose of this thesis is to investigate the use of optical angles data with and without laser ranging data in determining the trajectories of missiles. Analytical Graphics, Inc. Satellite Tool Kit is used to model the trajectory of a ballistic missile. Several scenarios are developed for determining the orbit when acquired by sensors providing various combinations of range, range rate and angles data. It is found that the combination of range, azimuth and elevation sensor data yields an orbit determination that has enough merit to be called accurate. The error of the orbit determined by the angles-only data is two orders of magnitude larger than the error of the range and angles measurement. Additionally completed was an analysis of what would happen if the sensors could only track to the maximum altitude of the orbit. As was assumed, the known position of the object drifts ranged from minimal to significant predicated on the final known position. This is indicated by the error ellipsoid. It was again found that the combination of range, azimuth and elevation sensor data until the maximum altitude yields an orbit determination that has enough merit to be called accurate. Also considered was the addition of a second sensor that had the capacity to always track range, azimuth and elevation to increase the time that is afforded to track the object, increasing the overall accuracy of the orbit determination. It is found that the addition of a second sensor increases the fidelity of the angles-only measurement such that the combination of azimuth and elevation sensor data yields an orbit determination that has enough merit to be called accurate.

Thesis. 1977. M.S.--Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND AERONAUTICS. / Includes bibliographical references. / M.S.

We can view quiver representations of a fixed dimension vector as an algebraic variety over an algebraically closed field $K$. There is an action of the product of general linear groups on each of these varieties where the orbits of the action correspond to isomorphism classes of quiver representation. A $K$-algebra $A$ is said to have the dense orbit property if for each dimension vector, the product of the general linear group acts on each irreducible component of the module variety with a dense orbit. Under certain conditions, a $K$ algebra $A$ is representation finite if and only if it $A$ has the dense orbit property. The implication representation finite implies the dense orbit property is always true. The converse is not true in general, as shown by Chindris, Kinser, and Weyman in \cite{ryan}. Our main theorem of this thesis builds on their work to give a family of representation infinite algebras with the dense orbit property. We also give a conjectured classification of indecomposables with dense orbits. \par In the future, we hope the work presented here can be used to find even more examples of representation infinite algebra with the dense orbit property to then develop deeper theory to classify algebras with the dense orbit property that are representation infinite.

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 154-157). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 154-157). Also available on the Internet.

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In chapter 3 of this thesis, I discuss in some detail the historical development of energy localization, emphasizing the particular physical concepts which are important for the understanding of this phenomenon. Furthermore, I describe the mathematical concepts of a discrete breather and homoclinic orbits, which are intimately connected between them and constitute the main object of study of this dissertation. / -

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