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Orbital Resonances In The Vinti Solution, Laura M. Duffy
Orbital Resonances In The Vinti Solution, Laura M. Duffy
Theses and Dissertations
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. …
Formation Flight Of Earth Satellites On Low-Eccentricity Kam Tori, Christopher T. Craft
Formation Flight Of Earth Satellites On Low-Eccentricity Kam Tori, Christopher T. Craft
Theses and Dissertations
The problem of Earth satellite constellation and formation flight is investigated in the context of Kolmogorov-Arnold-Moser (KAM) theory. KAM tori are constructed utilizing Wiesel’s Low-Eccentricity Earth Satellite Theory, allowing numerical representation of the perturbed tori describing Earth orbits acted upon by geopotential perturbations as sets of Fourier series. A maneuvering strategy using the local linearization of the KAM tangent space is developed and applied, demonstrating the ability to maneuver onto and within desired torus surfaces. Constellation and formation design and maintenance on KAM tori are discussed, along with stability and maneuver error concerns. It is shown that placement of satellites …