Date of Award
Master of Science
Department of Aeronautics and Astronautics
William E. Wiesel, PhD
This research uses the KAM theory that has been refined by Wiesel to show that Earth-satellites dynamics can be represented by an integrable Hamiltonian system with a small perturbation, like Earths geopotential. The satellite will follow a torus in phase space and remain on that KAM torus for all time unless acted on by a non-conservative force. A torus frequency was calculated, in this research, using a truth model in System Tool Kit (STK) and the High Precision Orbit Propagator (HPOP) to develop an accurate ephemeris file listing the Classical Orbital Elements (COEs). The frequencies found from the truth model were then used to calculate two delta-v maneuvers to insert a satellite onto a desired KAM torus at a specified position and time. Ultimately, this method could be a practical approach to the wider astronautics community to calculate a more accurate satellite position and time over longer periods when compared to current orbital mechanics methods. The results indicated that this particular scenario of fixing a satellite on a desired KAM torus using two delta-v maneuvers is not suitable. The residuals for the first test case were on the order of 107 or greater causing the satellite to lie on a different torus.
DTIC Accession Number
Reabe, Marissa C., "Formation Flight of Earth Satellites on KAM TORUS Using Classical Orbital Elements" (2017). Theses and Dissertations. 1721.