Bifurcation of Relative Equilibria in the Main Problem of Artificial Satellite Theory for a Prolate Body

Details Bifurcation of Relative Equilibria in the Main Problem of Artificial Satellite Theory for a Prolate Body Bifurcation of Relative Equilibria in the Main Problem of Artificial Satellite Theory for a Prolate Body

Dec 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002cemda..84..369l&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, v. 84, Issue 4, p. 369-385 (2002).

Astronomy and Astrophysics

Astronomy

J2 Problem, Periodic Orbits, Saddle-Center Bifurcation

Scientific paper

In this paper, we study circular orbits of the J2 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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