This paper considers the problem of optimizing low-thrust transfers to lunar orbits, to the libration points of the Earth–Moon system, and to the halo orbits around them. The goal of optimization is to minimize the thrust value. To solve the minimum-thrust problem, an indirect method based on the use of the maximum principle and the continuation method is used. The optimization problem for the considered type of trajectories gave rise to the necessity to overcome a number of problems associated with computational instability, limited size of the domain of existence of the solution and the necessity to choose the correct relation between the angular distance and the transfer duration in the geocentric and the selenocentric segments of trajectory. To overcome these difficulties, we propose to use a sequential solution of the problem of optimizing the limited power trajectories and the minimum-thrust problem in the formulation with the fixed angular distance and free transfer duration. The accuracy of calculating the derivatives that necessary to solve the boundary value problem of the maximum principle is ensured by the application of the automatic differentiation using complex dual numbers. The numerical examples of optimal direct and low-energy trajectories including the segment of motion along a stable manifold are given.


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    Titel :

    Minimum-Thrust Transfers to the Moon


    Weitere Titelangaben:

    Cosmic Res


    Beteiligte:

    Erschienen in:

    Cosmic Research ; 60 , 6 ; 481-490


    Erscheinungsdatum :

    2022-12-01


    Format / Umfang :

    10 pages




    Medientyp :

    Aufsatz (Zeitschrift)


    Format :

    Elektronische Ressource


    Sprache :

    Englisch




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