Generalized Focal–Type Orbital Elements Containing the Main Secular Effects Due to Oblateness
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Ignacio Aparicio [1] ; Luis Floría [2]
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[1] Universidad de Valladolid
Universidad de Valladolid
Valladolid, España
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[2] Universidad de Zaragoza
Universidad de Zaragoza
Zaragoza, España
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- Localización: XVII Congreso de Ecuaciones Diferenciales y Aplicaciones ; VII Congreso de Matemática Aplicada: Salamanca, 14-28 septiembre 2001 / coord. por Luis Ferragut Canals
, Anastasio Pedro Santos Yanguas , 2001, ISBN 8469961446, págs. 489-490 - Idioma: inglés
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Resumen
Within the framework of the linear and regular Celestial Mechanics, we consider the focal method canonical approach, thanks to which perturbed Keplerian systems with Deprit-like potentials admit exact linearization (reduction of the canonical equations of motion to harmonic-oscillator form, with respect to a true-like anomaly as the independent variable). Starting from harmonic-oscillator solutions to these exactly linearizable perturbations of the two-body problem, related to certain intermediary Hamiltonians arising in Artificial Satellite Theory, we deal with the Main Problem of this theory in terms of generalized focal elements linked to perturbed Keplerian systems with perturbations compatible with exact linearization. In linearizing focal-type DEF-variables, on incorporating the major J2 secular effects into our new orbital elements, we obtain generalized focal element equations, and apply them to the model of artificial satellite motion perturbed by the second zonal harmonic of the geopotential.
