Quasi-periodic orbits about the translunar libration point
Quasi-periodic orbits about the translunar libration point
复制标题
DOI：
10.1007/bf01227511
复制
发表时间：
1972-09
期刊：
影响因子：
--
通讯作者：
R. Farquhar;A. Kamel
中科院分区：
文献类型：
--
作者：
R. Farquhar;A. Kamel
利用Lindstedt-Poincaré方法和计算机代数运算，得到了关于月球平动点的拟周期轨道的解析解.这些解包括非线性、月球轨道偏心率和太阳引力场的影响。对于一个小振幅的轨道，从地球上看，轨道路径描绘出一个李萨如图形。这是由于平面内和平面外振荡的基频的微小差异。然而，当面内振荡的振幅大于32 379 km时，存在将产生基频相等的路径的面外振幅的对应值。这种同步轨道描述了月球的“光环轨道”。
Analytical solutions for quasi-periodic orbits about the translunar libration point are obtained by using the method of Lindstedt-Poincaré and computerized algebraic manipulations. The solutions include the effects of nonlinearities, lunar orbital eccentricity, and the Sun's gravitational field. For a small-amplitude orbit, the orbital path as viewed from the Earth traces out a Lissajous figure. This is due to a small difference in the fundamental frequencies of the in-plane and out-of-plane oscillations. However, when the amplitude of the in-plane oscillation is greater than 32 379 km, there is a corresponding value of the out-of-plane amplitude that will produce a path where the fundamental frequencies are equal. This synchronized trajectory describes a ‘halo orbit’ of the Moon.