The stability parameters of three-body periodic orbits

Abstract

Formulae containing the elements of the variational matrix are obtained which determine the linear ‘iso-energetic’ stability parameters of periodic orbits of the general three-body problem. This requires the numerical integration of the variational equations but produces the stability parameters with the effective accuracy of the numerical integration. The procedure is applied for the determination of ‘horizontally’ critical orbits among the members of sets of vertical-critical periodic orbits of the threebody problem. These ‘critical-critical’ orbits have special importance as they delimit the regions in the space of initial conditions which correspond to possibly stable three-dimensional periodic motion of low inclination.