Programed motion of the magnetized spacecraft

Abstract

This paper focuses on the problem of creation of control of the rotational motion of the magnetized dynamically symmetric Earth’s satellite in a polar circular orbit plane in the geomagnetic field. It is assumed that the permanent magnetic moment of the satellite is directed along the axis of its dynamic symmetry. The rotational motion of the satellite is caused by interaction of the magnetic moment of the satellite and the Earth’s magnetic field, which is modeled by the direct dipole. Influence of gravitational moment is not considered. The objective of the control system is to implement the required programed motion. The satellite’s rotation around its own axis is selected as the programed motion (in this case the angle deviation of the axis should be constant). Equations of programed motion of the magnetized satellite in the semi-combined coordinate system are derived. The control moments that ensure the specified programed motion are obtained. The solutions of the motion equations of the control system are found by Runge-Kutta method using the mathematical package Maple. According to the results the graphs of change of the kinematic parameters of the motion are obtained with and without control moments which demonstrate uncontrolled motion of the satellite. It is shown that the programed motion can be implemented by selection of the values of the deviation angle and the angular velocity, even when there is an asymptotic instability of Lyapunov’s programmed motion.