J2项摄动影响下的大气层外弹道规划改进算法
Trajectory planning algorithm of exo-atmosphere aircraft under the influence of the J2 perturbation

针对只限制飞行器始/终点位置和飞行时间两项约束条件的大气层外弹道规划问题, 提出了一种考虑地 球J2项引力摄动的Lambert改进制导算法. 根据经典Lambert制导理论确定中心力场假设条件下满足约束条件的标 准弹道轨迹, 然后与考虑地球扁率条件下的实际弹道轨迹相对比, 得到基于轨道参数的弹道偏差解析解. 通过设计 一种计及J2项引力摄动的虚拟目标点预测模型并补偿摄动偏差, 将引力摄动影响下的轨道规划问题重新转化到二 体理论Lambert制导下讨论. 与现有的摄动修正方法相比较, 考虑6个独立变量影响的预测模型修正算法能够全面完 整地反应出轨道参数对于轨道偏差的影响. 同时, 基于椭圆轨道参数的预测模型具有鲁棒性强、计算精度高以及计 算速度快等优点.
A modified Lambert algorithm considering the earth’s J2 perturbation gravitational is put forward for the trajectory planning problem of exo-atmosphere aircraft limited by two constraint conditions—the aircraft’s initial/terminal points and flight time. According to the classic Lambert guidance theory, the normal trajectory within the assumed condition of central gravitational force is determined to meet the constraint conditions. Then, comparing with the actual trajectory within earth’s oblateness perturbation, an analytic solution of trajectory deviation based on trajectory parameters is derived. By constructing a prediction model about the virtual terminal point in view of the J2 perturbation gravitational to correct the deviation of perturbation, the trajectory planning problem is covered to the discussion of Lambert problem within twobody theory. Comparing with the existing perturbation correction method, the modified algorithm of prediction model with 6 independent variables has a complete response to the influence between trajectory deviation and the parameters. At the same time, the prediction model has strong robustness, high accuracy and fast computation speed.