Analysis and control of satellite orbits around oblate Earth using perturbation method

Develops the dynamics of a particle satellite motion around the oblate Earth using a special rotating reference frame. The dynamics is used to deduce the conditions under which the orbital plane of motion of the particle satellite remains fixed. Next, a two-scale perturbation analysis is performed to seek the analytical solution of the particle satellite motion in the presence of the J₂ influence of the oblate Earth. The resulting analytical solution of the planar dynamics of the particle satellite is utilized to produce a planar motion controller so that the perturbation forces in the radial direction are tailored to guarantee that the particle satellite moves in a periodic trajectory. Finally, illustrative simulations are provided to demonstrate the effectiveness of the proposed framework