Spectral Decomposition of Orbital Tori

摘要

The Kolmogorov–Arnold–Moser theorem states that lightly perturbed integrable Hamiltonian systems maintainntheir multiply periodic, toroidal motion in the phase space. The assertion that Earth-orbiting satellites under theninfluence of the geopotential mimic this behavior is the underlying premise of this work. This paper focuses onnapplying trajectory-following spectral methods on selected orbits to decompose them into multiperiodic Fouriernseries, effectively compressing ephemerides for long-term use. The proposed approach focuses on fitting localnspectral structures, denoted as frequency clusters, within the sampled orbital data to the analytical form of thenwindowed, truncated, continuous Fourier transform. This approach is significantlymore numerically efficient thannfitting every coefficient within the N-tuple Fourier series simultaneously. Numerical simulations using integratedndata yield root-mean-square error in orbital tori fits at 10 m or less per coordinate axis over a one-year period fornmost low-inclination, low-eccentricity orbits with altitudes lower than 1900 km.