steady-state oscillations of a satellite with passive attitude control system in the magneto-lorentz coordinate system

In this paper, an artificial earth satellite with an electrodynamic attitude control system is considered. satellite attitude stabilization in the magneto-lorentz coordinate system is studied. the problem of the analytical construction of the periodic steady-state oscillations of the satellite in the passive control mode is solved. the solution is obtained in the form of a partial sum of trigonometric series. the algorithm for constructing solution is based on the introduction of auxiliary complex variables that make it possible to transform the initial non-autonomous differential equation of the 6th order to an autonomous differential system of the 8th order, for which the procedure for analytically finding the coefficients of a trigonometric series does not present fundamental difficulties, since it is reduced to sequential transformations using recurrent formulas. the constructed steady-state oscillations of the satellite make it possible to correct measurements of on-board instruments and increase the accuracy of information transmitted from the satellite.