Formation of a family of trajectories of free spherical motion of a spacecraft as a rigid body, providing reorientation of its axis of dynamic symmetry to a given position

DOI: 10.34759/trd-2021-121-02

Аuthors

Alimov N. I.^*, Gorbulin V. I.^*, Sudar Y. M.^*

Mlitary spaсe Aсademy named after A.F. Mozhaisky, Saint Petersburg, Russia

*e-mail: vka@mil.ru

Abstract

Analytical relations for trajectories parameters determining of the free (by inertia) spherical movement a satellite as a solid, which ensures reorientation of its dynamic axis of symmetry to the specified position in the regular precession mode, were obtained. A canonical inertial coordinate system, in which angles of orientation of the associated coordinate system, i.e. Euler angles, change in time linearly, was introduced. A peculiarity, explanating the ambiguity of determining the initial value of the rotation angle, is indicated, and the option of the pointed ambiguity elimination is suggested. The article demonstrates that spherical movement trajectory of a solid, which ensures the dynamic axis of symmetry retargeting to the required position in the predetermined time is a basic problem while reorientation control selection in the pulsing statement and computing required increment, kinetic moment and kinetic energy in the points of impulses application. The solutions being obtained allow assessing rather accurately the retargeting process duration and required energy consuming, necessary for further analysis. Besides, these solutions are a good initial approximation for the continuous control tasks. The authors introduced the notion of control strategy for spherical (angular) satellite motion control at lengthy time intervals, consisting of sequence of controls of the two active sections and ensuring transition from one angular motion trajectory to another, which kinematic and dynamic parameters are being determined based of the spacecraft flight program. The article proposes realizing continuous angular motion control computing at each active section based on the utilizing the concept of inverse problems of dynamics and algorithms for solving the problem two-pulse control of the satellite reorientation.

Keywords:

free spherical motion of a rigid body by inertia, canonical coordinate system, trajectory of angular motion, impulse control of angular motion, concept of inverse problems of dynamics

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