Locally optimal transfer trajectories between libration point orbits using invariant manifolds.

摘要

Techniques from dynamical systems theory and primer vector theory have been applied to the construction of locally optimal transfer trajectories between libration point orbits. When two libration point orbits have different energies, it has been found that the unstable manifold of the first orbit can be connected to the stable manifold of the second orbit with a bridging trajectory. A bounding sphere centered on the secondary, with a radius less than the radius of the sphere of influence of the secondary, was used to study the stable and unstable manifold trajectories. It was numerically demonstrated that within the bounding sphere, the two-body parameters of the unstable and stable manifold trajectories could be analyzed to locate low transfer costs. It was shown that as the two-body parameters of an unstable manifold trajectory more closely matched the two-body parameters of a stable manifold trajectory, the total DeltaV necessary to complete the transfer decreased. Primer vector theory was successfully applied to a transfer to determine the optimal maneuvers required to create the bridging trajectory that connected the unstable manifold of the first orbit to the stable manifold of the second orbit. Transfer trajectories were constructed between halo orbits in the Sun-Earth and Earth-Moon three-body systems. Multiple solutions were found between the same initial and final orbits, where certain solutions retraced interior portions of the trajectory. All of the trajectories created satisfied the conditions for optimality. The costs of transfers constructed using invariant manifolds were compared to the costs of transfers constructed without the use of invariant manifolds, when data was available. In all cases, the total cost of the transfers were significantly lower when invariant manifolds were used in the transfer construction. In many cases, the transfers that employed invariant manifolds were three to four times more efficient, in terms of fuel expenditure, than the transfer that did not. The decrease in transfer cost was accompanied by an increase in transfer time of flight. Transfers constructed in the Earth-Moon system were shown to be particularly viable for lunar navigation and communication constellations, as excellent coverage of the lunar surface can be achieved during the transfer.