基于摄动能量匹配条件的椭圆参考轨道伴飞构型设计

针对.J2摄动下椭圆参考轨道的稳定伴飞问题,提出了.J2摄动下的能量匹配条件,给出了迹向相对速度和径向相对位置的迭代设计方法,并设计了一种新的椭圆参考轨道伴飞构型.在此基础上,利用J2摄动下的能量匹配条件给出了计算伴飞初始相对状态的方法,并基于拉格朗日乘子法给出了位置保持脉冲的解析表达式,以获得形成稳定伴飞的初始相对状态和位置保持脉冲.仿真表明满足摄动能量匹配条件能形成稳定的伴飞构型,采用新的伴飞构型及其设计方法能明显减小分离距离的设计偏差.

Design of Leader-Follower Formation Near Elliptical Reference Orbit Based on Perturbed Energy Matching Condition

In order to keep perturbed relative motion stable, an energy matching principle under J2 perturbation is presented and two iteration methods for the along track relative velocity and radial relative position are developed. A new leader-follower formation and its initial relative states are designed according to the two proposed methods. Then an analytical expression of formation keeping impulse is derived based on Lagrangian multiplier method in order to mitigate the effect of formation initialization error. Simulation results show that the condition of energy matching under J2 perturbation can lead to a stable leader-follower formation. Furthermore, the new formation and its design method can reduce the designing error of separation distance.