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  • Analysis of the rotational motion of a uniaxial satellite due to magnetic and gravitational torques

    Paper ID



    • Michio Hara
    • Susumu Sawano


    Central Research Laboratory, Hitachi Ltd.






    In Japan, several projects are now under way for the development of scientific research satellites which will be launched into orbit in the near future. In some of these projects, it is required that the satellite spin axis be maintained normal to the orbit plane, or parallel to the Earth’s axis, to carry out scientific observations. The magnetic torquing methods have been considered attractive for this purpose because of simplicity and reliability. The magnetic methods, however, have been used for the satellites in the near-polar orbits [1,2], while the Japanese scientific satellites are to be launched into the comparatively low inclination orbits. This situation has necessitated the investigation of the general gyro-dynamics of a spinning satellite influenced by external torques in order to examine the applicability of the magnetic methods. In the first part of this paper, the equations of motion of a spinning uniaxial satellite responding to the mean magnetic and gravitational torques averaged over arbitrary portions of an eccentric orbit are derived. It is assumed in deriving them that the Earth’s magnetic field is represented by an uncanted dipole and that the satellite angular momentum vector coincides with the spin axis. A general phase trajectory of spin vector is obtained from these equations in the phase space which rotates synchronously with the orbit plane. In addition, a general solution is obtained for the case where only a magnetic torque exists. These analytical results are compared with certain of the observed motions of the known satellite.