Stability Study of a Relative Equilibrium in the Planar Circular Restricted Four-Body Problem

Abstract

Abstract We deal with the restricted planar four-body problem. That is, we consider motion of an infinitesimal small body (particle) under the Newtonian gravitational attraction of three bodies (primaries). It is supposed that primaries move in circular orbits forming Lagrange equilateral triangle; two of them have equal masses. By using the method of normal forms, we perform nonlinear stability study of a central configuration such that the particle is located in perpendicular bisector of the Lagrange equilateral triangle.