On Stability of Coplanar Libration Points in the Generalized Restricted Circular Tree-Bodies Problem

Alexander Rodnikov, Vladimir Beletsky

We study relative equilibria of a particle in vicinity of a rigid body, assuming the body motion about mass center is a regular precession. We model the body gravitation as gravitational field of two spheres with centers in the body axis of dynamical symmetry. We deduce the particle motion equations as two-parametrical generalization of Restricted Circular Problem of Three Bodies. We investigate stability of the particle equilibria called the Coplanar Libration Points in a plane crossing the spheres centers and the precession axis
if the spheres have equal masses.

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