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Hernández-Garduño, Antonio; Stoica, Cristina

Bifurcations of relative equilibria for one spheroidal and two spherical bodies. (English) Zbl 1284.70016

Astrophys. Space Sci. 343, No. 2, 523-534 (2013).
Summary: We discuss existence and bifurcations of non-collinear (Lagrangian) relative equilibria in a generalized three body problem. Specifically, one of the bodies is a spheroid (oblate or prolate) with its equatorial plane coincident with the plane of motion where only the “\(J_2\)” term from its potential expansion is retained.
We describe the bifurcations of relative equilibria as function of two parameters: \(J_2\) and the angular velocity of the system formed by the mass centers. We offer the values of the parameters where bifurcations in shape occur and discuss their physical meaning. We conclude with a general theorem on the number and the shape of relative equilibria.

Cited in 1 Document

MSC:

70F05 Two-body problems
70K50 Bifurcations and instability for nonlinear problems in mechanics
70F15 Celestial mechanics
70K42 Equilibria and periodic trajectories for nonlinear problems in mechanics

Keywords:

three body problem; spheroid; \(J_2\); Lagrangian relative equilibria; bifurcation
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