Transfers between libration-point orbits in the elliptic restricted problem

Details Transfers between libration-point orbits in the elliptic restricted problem Transfers between libration-point orbits in the elliptic restricted problem

Apr 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994cemda..58..317h&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 58, no. 4, p. 317-337

Astronomy and Astrophysics

Astronomy

4

Artificial Satellites, Celestial Mechanics, Lagrangian Equilibrium Points, Libration, Orbital Mechanics, Satellite Orbits, Spacecraft Maneuvers, Spacecraft Trajectories, Three Body Problem, Trajectory Analysis, Transfer Orbits, Center Of Gravity, Trajectory Optimization

Scientific paper

A strategy is formulated to design optimal time-fixed impulsive transfers between three-dimensional libration-point orbits in the vicinity of the interior L1 libration point of the Sun-Earth/Moon barycenter system. The adjoint equation in terms of rotating coordinates in the elliptic restricted three-body problem is shown to be of a distinctly different form from that obtained in the analysis of trajectories in the two-body problem. Also, the necessary conditions for a time-fixed two-impulse transfer to be optimal are stated in terms of the primer vector. Primer vector theory is then extended to nonoptimal impulsive trajectories in order to establish a criterion whereby the addition of an interior impulse reduces total fuel expenditure. The necessary conditions for the local optimality of a transfer containing additional impulses are satisfied by requiring continuity of the Hamiltonian and the derivative of the primer vector at all interior impulses. Determination of location, orientation, and magnitude of each additional impulse is accomplished by the unconstrained minimization of the cost function using a multivariable search method. Results indicate that substantial savings in fuel can be achieved by the addition of interior impulsive maneuvers on transfers between libration-point orbits.

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