KAM Torus Frequency Generation From Two-Line Element Sets

<p>The Kolmogorov Arnold and Moser (KAM) theorem states that a lightly perturbed Hamiltonian system will have solutions which lie on a torus. The trajectories of Earth orbiting satellites have been shown to lie on KAM tori with three basis frequencies. These basis frequencies are determined by fitting second order polynomials to data from Two-Line Element sets (TLEs) using a least squares technique. The first order coefficients are used as the torus basis frequencies while the second order coefficients are used to account for perturbations to the satellite's orbit such as air drag. Four cases are attempted using the Hubble Space Telescope and three rocket bodies as test subjects. A KAM torus with the desired basis frequencies is constructed and used to predict satellite position. This position prediction is compared to the position obtained from TLEs using Simplified General Perturbations 4 (SGP4) algorithms. Analysis of the torus position error shows that the torus construction algorithm does not fully characterize the contribution of the smaller basis frequencies to the orbital trajectory.</p><p>This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact and remains as true to the original work as possible. Therefore you will see the original copyright references library stamps (as most of these works have been housed in our most important libraries around the world) and other notations in the work.</p><p>This work is in the public domain in the United States of America and possibly other nations. Within the United States you may freely copy and distribute this work as no entity (individual or corporate) has a copyright on the body of the work.</p><p>As a reproduction of a historical artifact this work may contain missing or blurred pages poor pictures errant marks etc. Scholars believe and we concur that this work is important enough to be preserved reproduced and made generally available to the public. We appreciate your support of the preservation process and thank you for being an important part of keeping this knowledge alive and relevant.</p>