Elliptic relative equilibria in the N-body problem

Using these coordinates we study the linear stability of the elliptic relative equilibrium defined by the equilateral triangular central configuration of the three-body problem. We reproduce the analytic studies of G. Roberts. We also study the linear stability of the four- and five-body problem where three or four bodies of unit mass are at the vertices of a equilateral triangle or square and the remaining body is at the center with arbitrary mass μ.