Bifurcation of relative equilibria in the main problem of artificial satellite theory for a prolate body

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)369-385
Number of pages17
JournalCELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
Volume84
Issue number4
DOIs
StatePublished - Dec 1 2002
Externally publishedYes

Keywords

  • J problem
  • Periodic orbits
  • Saddle-center bifurcation

ASJC Scopus subject areas

  • Modeling and Simulation
  • Mathematical Physics
  • Astronomy and Astrophysics
  • Space and Planetary Science
  • Computational Mathematics
  • Applied Mathematics

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