On bifurcations and stability of central configurations in the planar circular restricted four-body problem

Abstract

The restricted four-body problem is considered. That is, we consider motion of an infinitely small body (particle) under the Newtonian gravitational attraction of three bodies (primaries). It is assumed that the primaries move in circular orbits, forming a stable equilateral Lagrange triangle. It is supposed that four bodies move in a plane. There exist relative equilibriums of the particle in the rotating with the primaries coordinate system. In such an equilibrium the particle forms a central configuration with the primaries. In the case of small mass ofa primary the bifurcations ofthe central configurations are investigated, as well as conditions oflinear stability for the central configurations is obtained. The study is performed analytically by using small parameter method.

Numerical Orbital Stability Analysis of Nonresonant Periodic Motions in the Planar Restricted Four-Body Problem

“…Thus, it is always unstable. The stability analysis of the configurations P 1 P 2 AP 3 and P 1 P 2 CP 3 has been performed in [8][9][10]. It was established that the configuration P 1 P 2 AP 3 is unstable for any possible values of μ.…”