TRANSFERS BETWEEN CALIBRATION-POINT ORBITS IN THE ELLIPTIC RESTRICTEDPROBLEM

A strategy is formulated to design optimal time-fixed impulsive transf ers between three-dimensional libration-point orbits in the vicinity o f the interior L1 libration point of the Sun-Earth/Moon barycenter sys tem. The adjoint equation in terms of rotating coordinates in the elli ptic restricted three-body problem is shown to be of a distinctly diff erent form from that obtained in the analysis of trajectories in the t wo-body problem. Also, the necessary conditions for a time-fixed two-i mpulse transfer to be optimal are stated in terms of the primer vector . Primer vector theory is then extended to non-optimal impulsive traje ctories in order to establish a criterion whereby the addition of an i nterior impulse reduces total fuel expenditure. The necessary conditio ns for the local optimality of a transfer containing additional impuls es are satisfied by requiring continuity of the Hamiltonian and the de rivative of the primer vector at all interior impulses. Determination of the location, orientation, and magnitude of each additional impulse is accomplished by the unconstrained minimization of the cost functio n using a multivariable search method. Results indicate that substanti al savings in fuel can be achieved by the addition of interior impulsi ve maneuvers on transfers between libration-point orbits.