The stability parameters of three-dimensional periodic three-body orbits

Abstract

Formulae containing the elements of the variational matrix are obtained which determine the linear ‘isoenergetic’ stability parameters of three-dimensional periodic orbits of the general three-boy problem. This requires the numerical integration of the variational equations but produces the stability parameters with the effective accuracy of the numerical integration. The conditions for stability, criticality, and bifurcations are briefly examined and the stability determination procedure is tested in the determination of some three-dimensional periodic orbits of low inclination bifurcating from vertical-critical coplanar orbits.