The Translation of the Vehicle With a Controlled Thrust Vector to a Given Landing Location With Minimal Fuel Consumption

The problem of vehicle’s translation to a certain landing location above the surface of the planet is considered. Using the Pontryagin maximum principle, the optimal control problem is reduced to a boundary value problem for a system of nonlinear differential equations. A qualitative analysis of the optimal phase trajectories of the system is carried out, their properties are established, illustrated by the results of numerical modeling. The domains in the plane of phase variables are analytically described, from which it is possible to achieve a terminal set. A synthesis of optimal control is constructed.