In this paper, the problem of optimization of multi-revolutionary transfers of a spacecraft with a fixed angular range of auxiliary longitude and the free transfer time from a given initial orbit to geostationary orbit in a central Newtonian gravitational field is considered. The purpose of the optimization is to calculate the program of control of the vector of the thrust, which provided optimal multi-revolutionary trajectories to the final orbit with the minimum cost of the propellant. The magnitude of thrust is assumed to be constant. The optimized control is the vector control program of thrust, including its direction and periods of operation. For mathematical modeling of the spacecraft motion, differential equations in equinoctial elements are used, and as an independent variable, an auxiliary longitude is used, introduced in such a way that the differential equation for it coincides with the differential equation for true longitude in unperturbed motion. An approach based on the Pontryagin maximum principle is proposed to solve the trajectory optimization problem. Using the maximum principle, the problem of optimizing the multi-revolutionary transfer of spacecraft with limited thrust is reduced to a two-point boundary value problem and the boundary value problem is solved by the method of continuation on parameter. To get the goal, the problems of optimizing the multi-revolutionary transfer with limited power and limited thrust are considered.

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