This work studies the optimum rendezvous with minimum fuel consumption two space vehicles on circular and elliptical orbits, the surveyor vehicle being equipped with a low thrust installation, their motion equations being written in the three-dimensional space, in relative motion; the space origin being the target vehicle. Optimal controls to be determined being the acceleration due to thrust related to the minimum fuel consumption. By means of the Legendre-Clebsch condition it is demonstrated that the formulated optimization problem is, indeed, a minimum problem. [References: 2]
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