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Orbital Tori Construction Using Trajectory Following Spectral Methods, Ralph E. Bordner Iii
Orbital Tori Construction Using Trajectory Following Spectral Methods, Ralph E. Bordner Iii
Theses and Dissertations
By assuming the motion of a satellite about the earth’s geopotential mimics the known Kolmogorov-Arnold-Moser (KAM) solution of a lightly perturbed integrable Hamiltonian system, this research focused on applying trajectory following spectral methods to estimate orbital tori from sampled orbital data. From an estimated basis frequency set, orbital data was decomposed into multi-periodic Fourier series, essentially compressing ephemerides for long-term use. Real-world Global Positioning System (GPS) orbital tracks were decomposed and reconstructed with error from as low as few kilometers per coordinate axis over a 10-week span to tens of kilometers per coordinate axis over the same time period, depending …
Relative Orbit Elements For Satellites In Elliptical Orbits, Kirk W. Johnson
Relative Orbit Elements For Satellites In Elliptical Orbits, Kirk W. Johnson
Theses and Dissertations
The purpose of this research was to describe the unperturbed relative motion of Earth satellites in elliptical orbits using a simple dynamics model whose parameters allow significant geometrical insight and operational efficacy. The goal was to retain the advantages of the Relative Orbit Elements (ROE) realization of the Hill-Clohessy-Wiltshire (HCW) equations, a linearized dynamics model for circular reference orbits. Specifically, this thesis analyzed the geometry of satellite rendezvous and proximity operations using the ROE parameters to characterize the model’s utility. Next, through a comprehensive literature review, this thesis sought possible approaches for developing a similarly useful parameterization for chief orbits …
Verification Of Kam Theory On Earth Orbiting Satellites, Christian L. Bisher
Verification Of Kam Theory On Earth Orbiting Satellites, Christian L. Bisher
Theses and Dissertations
This paper uses KAM torus theory and Simplified General Perturbations 4 (SGP4) orbit prediction techniques compiled by Dr. William Wiesel and compares it to Analytical Graphics ® Incorporated (AGI) Satellite Toolkit ® (STK) orbit data. The goal of this paper is to verify KAM torus theory can be used to describe and propagate an Earth satellite orbit with similar accuracy to existing general perturbation techniques. Using SGP4 code including only truncated geopotential effects, KAM torus generating code, and other utilities were used to describe a particular satellite orbit as a torus and then propagate the satellite using traditional and KAM …