Optimal transfers between librationpoint orbits in the elliptic restricted threebody problem
Abstract
A strategy is formulated to design optimal impulsive transfers between threedimensional librationpoint orbits in the vicinity of the interior L(1) libration point of the SunEarth/Moon barycenter system. Two methods of constructing nominal transfers, for which the fuel cost is to be minimized, are developed; both inferior and superior transfers between two halo orbits are considered. The necessary conditions for an optimal transfer trajectory are stated in terms of the primer vector. The adjoint equation relating reference and perturbed trajectories in this formulation of the elliptic restricted threebody problem is shown to be distinctly different from that obtained in the analysis of trajectories in the twobody problem. Criteria are established whereby the cost on a nominal transfer can be improved by the addition of an interior impulse or by the implementation of coastal arcs in the initial and final orbits. The necessary conditions for the local optimality of a timefixed transfer trajectory possessing additional impulses are satisfied by requiring continuity of the Hamiltonian and the derivative of the primer vector at all interior impulses. The optimality of a timefree transfer containing coastal arcs is surmised by examination of the slopes at the endpoints of a plot of the magnitude of the primer vector over the duration of the transfer path. If the initial and final slopes of the primer magnitude are zero, the transfer trajectory is optimal; otherwise, the execution of coasts is warranted. The position and timing of each interior impulse applied to a timefixed transfer as well as the direction and length of coastal periods implemented on a timefree transfer are specified by the unconstrained minimization of the appropriate variation in cost utilizing a multivariable search technique. Although optimal solutions in some instances are elusive, the timefixed and timefree optimization algorithms prove to be very successful in diminishing costs on nominal transfer trajectories. The inclusion of coastal arcs on timefree superior and inferior transfers results in significant modification of the transfer time of flight caused by shifts in departure and arrival locations on the halo orbits.
 Publication:

Ph.D. Thesis
 Pub Date:
 September 1992
 Bibcode:
 1992PhDT........66H
 Keywords:

 Libration;
 Orbital Mechanics;
 Three Body Problem;
 Trajectory Optimization;
 Transfer Orbits;
 Algorithms;
 Center Of Gravity;
 Hamiltonian Functions;
 Impulses;
 Astrodynamics