The problem of satellite attitude stabilization in the geomagnetic field

A satellite moving along a circular Keplerian orbit in near-Earth space was explored, focusing on its attitude stabilization in the orbital coordinate system using the intrinsic magnetic and Lorentz force moments. Fluctuations in geomagnetic induction that occur as the satellite orbits cause the coefficients in the dynamical equations governing the satellite’s attitude motion to vary over time. The results show that, although the linearized system of differential equations of the satellite’s motion is non-stationary, it can be reduced to a stationary system of higher order, which holds even for high-precision multipole models of the geomagnetic field. Thus, a control law design was proposed to stabilize the satellite. The controllability of the system was analyzed, and an optimal stabilization algorithm based on the LQR method was developed. The effectiveness of the proposed approach was validated by computer modeling.