Exact linearization of non-planar intermediary orbits in the satellite theory |
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| Authors: | José Manuel Ferrándiz Ana Fernández-Ferreiros |
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| Institution: | (1) Departamento de Matemática Aplicada a la Ingeniería, E.T.S. de Ingenieros Industriales, Universidad de Valladolid, 47011 Valladolid, Spain;(2) Departamento de Matemática Aplicada, E.TS. de Ingenieros Industriales, Universidad de Zaragoza, 50015 Zaragoza, Spain |
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| Abstract: | In this paper we consider the reduction of the equations of motion for non-planar perturbed two body problems into linear form. It is seen that this can be easily accomplished for any element of the class of radial intermediaries to the satellite problem proposed by Deprit in 1981, since they have a functional dependence suitable for linearization. The transformation is worked out by using an adequate set of redundant variables. Four harmonic oscillators are obtained, of which two are coupled through gyroscopic terms. Their constant frequencies contain the secular contribution of the main problem of artificial satellite theory up to the order of the considered intermediary. Therefore, this result may well be interesting in relation to the study and prediction of accurate long-term solutions to satellite problems. |
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| Keywords: | Artificial satellites radial intermediary linearization |
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