Evaluation of Asymmetric Small Satellite with Electric Propulsion Perturbations when Passing through Resonance

Motion of a low circular orbit asymmetric microsatellite with electric propulsion is considered. During slow deceleration of microsatellite within the passive part of its flight in the upper atmosphere, the frequencies characterizing its rotational motion may coincide. It is known that the main resonance, i.e. resonance of the lowest order, has the greatest influence on motion of microsatellite around the center of its mass. Presence of small aerodynamic asymmetries of microsatellites results in disturbances in the angle of attack that occur when passing through the main resonance. Perturbations of the value of attack angle can lead to significant deviations from nominal trajectory at the stage of active use of electric propulsion, or loss of stability of the angular motion of a microsatellite. In order to investigate motion of a microsatellite relative to the center of mass, a low-frequency system of motion equations is applied. This system of equations adequately describes rotational motion of the microsatellite with provision for the main resonance at angles of attack not exceeding 90 degrees. As the final result, we obtain analytical estimates of attack angle perturbations when passing through the main resonance in case of considerable angles of attack. Numerical results confirm adequacy of the approximate analytical estimation.