Halo轨道Richardson三阶近似解析解的改进

The Improvement of Richardson's Three Order Approximate Analytical Solution of Halo Orbit

Halo轨道可以用来进行观测太阳活动,观测月背面,地月中继通信等航天任务。Richardson的三阶近似解析解是共线平动点的Halo轨道确定的基础。Richardson解析解是基于一种Lindstedt-Poincaré法的消去长期项的方法,在保留三阶小量方程中,假设角频率和位移展开到数量级第三级,并通过依次提取数量级相同的变量构成的方程进行推导的。在Richardson的解析解中,数量级第1级和第2级方程以及第3级在z轴方向的方程都消去了长期项,然而数量级第3级在x和y方向上并没有消去长期项。提出了Richardson三阶近似解析解的一种改进解析解,其数量级第3级在x和y轴上的分量比Richardson解析解更精确。并通过Matlab的数值计算验证了改进解析解的优势。

Halo orbit could be used to process astronautics assignments, such as observation to the movement of the sun and the back of the moon, the communication between the earth and moon, and so on. Richardson＇s third order approximate analytical solution was the foundation of the determination of Halo orbit. Richardson＇s solution was based on Lindstedt-Poincaré method, and the method was used to remove the secular terms. In the reset＂red third order little magnitude equations, the solutions of angle frequency and the displacement were supposed to expand into third order. The same magnitude would be collected in same equation. In Richardson＇s solutions, the secular terms were removed in the first and second magnitude equations and the z direction of the third magnitude equation, but not removed in the x and y direction of the third magnitude equation. The improved analytical solution better than Richardson＇s third order approximate analytical solution is brought forward, and components in the x and y direction of the third order of the improved analytical solution are more exact than Richardson＇s analytical solution. The advantage of the improved analytical solution is verified by Matlab numerical simulation.