Date of Award
Master of Science
Department of Aeronautics and Astronautics
William E. Wiesel, Jr., PhD.
This research applies KAM theory to highly eccentric orbits for earth orbiting satellites by using spectral methods to find the three basis frequencies resulting from earth's geopotential. Once a torus is created from these frequencies, its dynamics data can be compared to the position data of an integrated data set over multiple orbit types, specifically, orbits with varying eccentricity. The analysis shows that many eccentric orbits are actually KAM tori when the only perturbation is the earth's geopotential. The residuals agree to 10s of meters in most cases. This research also outlines many of the limitations of the current method and gives recommendations for further study and real-world applications. Applications focus on space debris and non-operational satellites.
DTIC Accession Number
Dunk, Adam B., "Applying KAM Theory to Highly Eccentric Orbits" (2014). Theses and Dissertations. 744.