卫星编队飞行中Lawden方程的误差分析  

ERROR ANALYSIS OF LAWDEN’S EQUATIONS IN SATELLITE FORMATION FLYING

作　　者：崔海英[1] 李俊峰[1] 高云峰[1] 

机构地区：[1]清华大学航天航空系,北京100084

出　　处：《工程力学》2006年第12期188-192,共5页Engineering Mechanics

基　　金：国家自然科学基金资助项目(10202008);高等学校博士学科点基金资助项目(20020003024)

摘　　要：从Lawden方程的建立着手,分析了方程的模型误差。通过对Lawden方程与数值积分两种方法得到的相对轨迹进行比较,指出了Lawden方程解的非周期性,以及为满足解的周期性而选取的初始条件是一个与满足长期编队条件没有必然关系的强制条件。并通过计算从星能量变化确定方程解的精度,提出了通过约束相对轨迹的大小来保证设计精度这一控制误差的方法。仿真结果证明了方法的正确性。Lawden＇s equations are firstly established to investigate the model error. By comparing the relative trajectory calculated by the Lawden＇s equations and that by numerical integral method, it is concluded that the homogenous solutions of Lawden＇s equations are non-periodical, and the initial condition, which is selected to satisfy the periodical solutions, is a compulsory one irrelevant to the condition of long-term formation flying. The precision of the equations＇ solutions is specified by calculating the energy variation of the follower satellite, and a method that guarantees the design precision by constraining the size of the relative trajectory is proposed. The simulation results show that the proposed method is effective.

关 键 词：航天器飞行力学 卫星编队飞行 Lawden方程 模型误差 相对轨迹 周期性解 

分 类 号：V412.4[航空宇航科学与技术—航空宇航推进理论与工程]