Abstract
A direct method for optimizing the spatial trajectories of lunar landing in the deceleration phase with a limitation along the descent profile, when the lander must remain inside a certain cone with apex at a given landing point, is presented. The model of motion is a point of variable mass moving in a uniform gravitational field. The method uses a two-level optimization of the characteristic velocity for a given distance and lateral displacement at free landing time. The upper level corresponds to one-dimensional nonlinear optimization of the landing time. The lower level corresponds to optimization for the landing times established at the upper level and the given coordinates of the landing point using discrete sets of pseudopulses and high-dimensional linear programming. Energetically accessible regions and regions when redetermining the landing point are presented as examples.
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