Relative dynamics and initialization condition for formation flying in elliptical orbits

Hill equations have definite limitation in the design of satellite formation flying in elliptical orbits, to solve this problem, the design method of satellite formation flying in circular orbits based on Hill equation can be generalize and applied to the formation flying in elliptical orbits. T-H equation is expressed as the explicit function form of reference orbit true anomaly, and the state transition matrix of relative motion of satellite formation flying in elliptical orbits is derived. According to the requirement that relative dynamics equation of satellite formation flying in elliptical orbits has periodicity solution, the general initialization condition of periodicity motion that satellite formation flying in elliptical orbits is discussed. Finally, based on the theoretical results, some numerical simulations are carried out. The initialization condition derived can be applying in initial design of formation flying in elliptical orbits or relative motion error estimation.