Primer vector theory in the design of optimal transfers involving libration point orbits

Julia Lea Bell, Purdue University

Abstract

Optimal impulsive transfers between libration point orbits associated with the same libration point are considered in the circular and elliptic restricted three-body problems. Existing primer vector theory is applied in conjunction with numerical integration and differential corrections techniques to construct optimal trajectories. The necessary conditions for optimality are stated in terms of the primer vector. Coast arcs and interior impulses are employed simultaneously to improve non-optimal paths. Both superior and inferior optimal transfers in the Sun-Earth problem are achieved for $ L\sb1$ halo orbits with out-of-plane amplitudes in the range of 110,000 km to 800,000 km. Unconstrained numerical optimization techniques are used to compute the optimal coast arcs and the optimal timing and location for interior impulses. A gradient-based algorithm is employed where the gradients are evaluated from analytic expressions that are functions of the primer vector and its time derivative. Differential corrections techniques are developed to solve point-to-point targeting problems that occur within the optimization process. Families of optimal transfers are presented that include various target orbits that are characterized by the out-of-plane amplitude. Two classes of optimal solutions are presented. Optimal solutions requiring two impulses are computed for transfers between L$\sb1$ northern halo orbits where the transfer path exists above the plane of primary motion. Optimal solutions requiring three impulses are presented for transfers between L$\sb1$ northern orbits where the transfer occurs below the plane of primary motion. The optimal costs are plotted versus the amplitudes of the target orbits. A linear function that approximates the relationship between the transfer cost and the target amplitude is identified for transfers in each class.

Degree

Ph.D.

Advisors

Howell, Purdue University.

Subject Area

Aerospace materials

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