Optimal formation reconfigurations subject to hill three-body dynamics

The article presents fuel-optimal continuous thrust formation flying maneuvers near the L₂ Lagrangian point of the Hill restricted three-body dynamics. Under mild assumptions of the analyticity of the performance index and dynamical system, the generating function approach provides the initial adjoint and the optimal control in series form, with respect to known boundary conditions and time index. It is numerical in the sense that the initial value problems are solved for a system of ordinary differential equations numerically, and is analytic in the sense that the solution in explicit series form can be directly evaluated for desired boundary conditions and time spans. The higher-order solution obtained from the generating function provides more precise results and a larger region of temporal/spatial convergence than the linear quadratic solution.