Optimal Transfers Between Periodic Orbit Families

A general optimization framework for targeting families of periodic orbits is developed. The framework exploits a parametrization method that provides the states and partial derivatives of periodic orbits as a function of phase and family variables, enabling transfers that are optimal across families as whole. The same parameterization is used to generate initial guesses that allow convergence of multi-revolution transfers in unstable families where ballistic guesses fail. The framework is independent of the specific parameterization or direct optimization method, making it adaptable to a variety of approaches. Although applicable to any two-dimensional manifold of pre-computed orbits, the contents of this work focuses on transfers between common periodic orbits within the Earth–Moon system. Representative periodic-orbit families relevant to this work include distant retrograde orbits (DROs), the L1 and L2 Lyapunov families, and the L1 and L2 south halo families. This framework enables automated construction of multi-revolution trajectories between and across periodic-orbit families, eliminating the need for extensive up-front dynamical-systems analysis.