Abstract
The problem of optimal use of a tether to increase the final energy of a payload is posed. The optimal solution must consist of zero tension arcs, full tension arcs, and possibly singular arcs. For a massless tether, the state solution can be obtained for both full tension and free arcs, reducing the system to a parameter optimization problem. Optimal trajectories begin with a coasting arc to obtain separation between the payload and the orbiter, and then the payload is accelerated toward the orbiter with positive cable tension. Optimal lofting trajectories thus require reel-in deployment systems. Example solutions are given for several values of the cable tension. The maximum reel-in speed at the winch device is always a substantial fraction of the payload release speed.
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