Date of Award


Document Type


Degree Name

Master of Science


Department of Aeronautics and Astronautics

First Advisor

William E. Wiesel, PhD.


The Vinti Solution offers a more accurate model than the two-body problem as an orbital propagator. Unfortunately, the Vinti solution contains small divisors near orbital resonances in the perturbative terms of the Hamiltonian, which lead to inaccurate orbital predictions. One approach to avoid the small divisors is to apply transformation theory. The methodology of this research is to identify the perturbative terms of the Vinti Solution, perform a coordinate transformation, and derive the new equations of motion for the Vinti system near orbital resonances. The analysis in this research focuses on the 2:1 resonance, which includes the Global Positioning System. The phase portrait of a nominal Global Positioning System satellite orbit is found to contain a libration and chaotic region. Further analysis shows that the dynamics of the 2:1 resonance affects orbits with semi-major axes ranging from -5.0 to +5.4 kilometers from an exactly 2:1 resonant orbit. Truth orbits of seven Global Positioning System satellites are produced for 10 years. Two of the satellites are found to be outside of the resonance region. Three are found to be influenced by the libration dynamics of the resonance. The final satellite is found to be influenced by the chaotic dynamics of the resonance.

AFIT Designator


DTIC Accession Number


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Astrodynamics Commons