Optimal low-thrust, limited power transfers between arbitrary elliptical orbits

An attempt is made to generalize Edelbaum's method of calculating optimal coplanar and coaxial orbital transfer to arbitrary elliptical orbits. The notion of 'average Hamiltonian' is introduced to derive general equations of motion for optimal transfer trajectories. Assuming a fixed transfer duration sufficiently long to allow a large number of revolutions around the planet, the equations are reduced to a second order differential system followed by two quadratures. The solution of the general transfer problem, which is further reduced to the orientation-shape sub-problem, as well as the computation of the conjugate point can be carried out by numerical methods. Analytical solutions are examined for the particular cases of the coplanar, coaxial and coparameter transfers, and the linearized problems near these cases. Particular attention is given to the transfers from a circular orbit and between two symmetric orbits.