Aerodynamic Torque Exhibits Resonance in Satellite Motion

This paper deals with the non-linear oscillation of a satellite in an elliptic orbit around the Earth under the influence of aerodynamic and gravitational torque. It is assumed that the orbital plane of the satellite coincides with the equatorial plane of the Earth. The main and parametric resonances exist and are numerically solved using variation of parameters method. It is observed that discontinuity occurs in the amplitude at a frequency of the external periodic force which is less than the frequency of natural oscillations. The 2D and 3D resonance curves are plotted for main resonance at n ≈ 1. From resonance plots, it is observed that as eccentricity and aerodynamic torque increases, the jump in amplitude increases which shows that the aerodynamic torque and eccentricity plays an important role in changing the orbital parameters of the satellite. For Earth satellite system, the existence of 1:2 mean motion resonance concludes that different frequency states transit the regular motion into chaotic state. Thus it is concluded that aerodynamic torque parameter plays an important role in changing regular motion of satellite into chaotic motion.