The fastest reorientation of the spacecraft's circular orbit plane

DOI: 10.34759/trd-2020-113-16

Аuthors

Pankratov I. A.

Saratov State University named after N. G. Chernyshevsky, 83, Astrakhanskaya str., Saratov, 410012, Russia

e-mail: PankratovIA.mechanic@gmail.com

Abstract

The article considers the problem of the fastest reorientation of the spacecraft’s circular orbit plane in quaternion formulation. The spacecraft orbit terminal position is not being fixed in the orbit plane. Control, i.e. the acceleration from the jet thrust vector, orthogonal to the orbit plane, is a piecewise-constant function, limited in absolute value. The spacecraft center of mass motion is described by the quaternion differential equation of orientation of the orbital system of coordinates. The article presents an original genetic algorithm, developed by the author, for finding the number of active section of a spacecraft movement and their duration. While this technique application there is no need in searching for the initial values of the unknown initial values of conjugate variables. To solve the Cauchy problem at one of the algorithm operation stages, a well-known partial solution of the quaternion differential equation of orientation of the orbital system of coordinates was used. Examples of the problem numerical solution are presented. A case, when the difference between initial and final orientations of the spacecraft orbit is units of degrees in the angular measure is considered. The final orientation of the spacecraft orbit plane herewith corresponds to the orbit plane of the satellites of the Russian GLONASS orbital grouping. Graphs of components of the quaternion of orientation of the orbital system of coordinates, angular variables, describing orientation of the spacecraft orbit plane, and optimal control are plotted. Specific features and regularities of the optimum reorientation process of the spacecraft orbit plane are established.

Keywords:

spacecraft, orbit, optimization, quaternion, gene

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