Stochastic Orbit Prediction Using KAM Tori
Max William Yates
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Stochastic Orbit Prediction Using KAM Tori

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Kolmogorov-Arnold-Moser (KAM) Theory states that a lightly perturbed, conservative, dynamical system will exhibit lasting quasi-periodic motion on an invariant torus. Its application to purely deterministic orbits has revealed exquisite accuracy limited only by machine precision. The theory is extended with new mathematical techniques for determining and predicting stochastic orbits for Earth satellite systems. The linearized equations of motion are developed and a least squares estimating environment is pioneered to fit observation data from the International Space Station to a phase space tr...