共线平动点附近周期轨道的分析研究方法  

Analyzing the periodic orbits around the collinear liberation points

作　　者：张守余[1] 杜兰[1] 

机构地区：[1]信息工程大学测绘学院,郑州450052

出　　处：《测绘科学》2009年第3期61-63,共3页Science of Surveying and Mapping

摘　　要：首先介绍了圆型限制性三体问题的非线性常微分运动方程组,利用定性分析方法、级数解法和数值解法,系统地介绍了这个问题的求解分析方法,相应地给出了共线平动点附近的力学特性、条件周期(和拟周期)轨道,并通过分析一个周期处的状态转移矩阵(Monodromy矩阵)分析了各类轨道的稳定性以及几种周期和拟周期轨道之间的关系。另外,还给出了圆型限制型三体模型下Halo轨道的牛顿迭代算法。Based on the non-linear differential equations of the CRTBP, three kinds of methods, namely, qualitatively analyzing method, series expension method and numerical method, are introduced to analyze the dynamic eharaetoresties, periodic and quasi-periodic orbits around the collinear libration points within the CRTBP. The monodromy matrix is investigated to discuss the stability and relationships between the periodic orbits and their surounding quasi-periodic orbits. Moreover, the Newton iteratrion method is introduced to search and construct the well-known Halo orbit in CRTBP.

关 键 词：圆型限制性三体问题 共线平动点 Lindstedt—Poincare方法 M矩阵 HALO轨道 

分 类 号：P228[天文地球—大地测量学与测量工程]