Bifurcation of Relative Equilibria in the Main Problem of Artificial Satellite Theory for a Prolate Body |
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Authors: | Cédric Langbort |
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Institution: | (1) Department of Theoretical & Applied Mechanics, Cornell University, 212 Kimball Hall, Ithaca, NY, 14853 |
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Abstract: | In this paper, we study circular orbits of the J
2 problem that are confined to constant-z planes. They correspond to fixed points of the dynamics in a meridian plane. It turns out that, in the case of a prolate body, such orbits can exist that are not equatorial and branch from the equatorial one through a saddle-center bifurcation. A closed-form parametrization of these branching solutions is given and the bifurcation is studied in detail. We show both theoretically and numerically that, close to the bifurcation point, quasi-periodic orbits are created, along with two families of reversible orbits that are homoclinic to each one of them. |
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Keywords: | J
2 problem periodic orbits saddle-center bifurcation |
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