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Journal of Automation and Information Sciences
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ISSN Print: 1064-2315
ISSN Online: 2163-9337

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Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v33.i11.50
13 pages

Averaging of Motion Equations in the Problem of Optimization with Respect to Operating Speed of Interorbital Transfer with Thrust of Constant Value in a Strong Central Gravity Field

Boris N. Kiforenko
S.P. Timoshenko Istitute of Mechanics of National Academy of Sciences of Ukraine, Kiev, Ukraine
Zoya V. Pasechnik
Kyiv National Taras Shevchenko University, Kyiv, Ukraine
Igor Yu. Vasil'ev
Kyiv National Taras Shevchenko University, Kyiv, Ukraine

ABSTRACT

We consider the problem about the minimum time for transfer of a spacecraft with low thrust of constant value, which is regulated with respect to direction between arbitrary elliptic orbits in a central force field. We do not superimpose restrictions on position of the spacecraft for initial and terminal orbits. The analysis of the optimal control is carried out with application of the Pontryagin maximum principle. Taking into account specific peculiarities of motion with low thrust and large promptness around the center of gravity we make use of the Bogolyubov-Mitropolskiy method. In contrast to well-known solution by Edelbaum we succeeded to write down analytically the averaged equations of the optimal motion of the first approximation. By means of well-known first integrals and the new integral of averaged motion equations the corresponding two-point boundary problem was reduced to a form, which demands integration of the system of differential equations of the fourth order and determination of four unknown constants.


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