月球中继通信大椭圆冻结轨道偏心率全局搜索设计研究

A dual-layer optimization approach is put forward to meet the relay communication requirements of the fourth-phase mission of the lunar exploration program，with the aim of designing high lunar frozen orbits utilizing concentric-circle phase diagrams of Hamiltonian systems. Within the framework of a high-order lunar gravitational field model raised to the 15th order，the canonical form of Hamiltonian equations is depicted by employing Delaunay variables. By applying the Hori-Lie transformation，perturbation equations with short-period terms removed are formulated，and concentric-circle phase diagrams of Delaunay variables are derived based on the properties of equilibrium points. Moreover，a dual-layer optimization algorithm that combines the iterative search of concentric-circle phase diagrams with particle swarm optimization （PSO） is devised. This algorithm is integrated with long-term evolution data under the ephemeris model and the mean-osculating orbit element interchange method. It is used to screen out the lunar relay mission orbits with the most favorable frozen characteristics. During an 8-year long-term evolution simulation under the ephemeris model，the dual-layer optimization algorithm effectively curtails the drifts of orbital elements and the decline of perilune altitude. As a result，the 24-hour mission orbit with the optimal frozen characteristics is obtained，offering a valuable reference for the orbit design of long-duration lunar relay communication systems.