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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 …