Low Energy Transit Orbits in the Restricted Three-Body Problems
Low Energy Transit Orbits in the Restricted Three-Body Problems
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DOI：
10.1137/0116060
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发表时间：
1968-07
影响因子：
1.9
通讯作者：
C. Conley
中科院分区：
文献类型：
--
作者：
C. Conley
1.导论.这项工作涉及轨道的限制性三体问题;为讨论这个问题的读者是指[2]，[3，章。[6]和[4]。这里特别感兴趣的是在这三个临界点附近对应于共线拉格朗日点的轨道的行为，特别是那些Jacobi常数刚好大于临界点的轨道。对应于这些雅可比常数值的希尔区域包含一个关于拉格朗日点的“颈”;因此，在质量点之间的拉格朗日点的情况下，积分表面上的轨道可以从一个质量点到另一个质量点（通过颈）。这里的目的是描述”脖子”上的轨道。这项工作的目的是双重的。首先，在[5]中，考虑了一个具有不稳定临界点的一般Hamilton系统（具有两个自由度），并且用某些圆盘映射描述了关于临界点的最终行为或轨道。在这项工作中，圆盘结构出现在限制问题中的方式被描述，以便[5]的结果可以解释这个问题。第二个目的是提出一个低能量地月轨道设计方案。关于这个问题的数值计算工作已经开始，将在以后的文章中叙述;现在只叙述一般的格式（4）。为了对”颈”（以后称为平衡区）中轨道的出现有一个好的概念，讨论在临界点附近线性化的运动方程就足够了。实际上，由于J. Moser对A. Liapounoff（见[6]）这样一个讨论的所有定性结果都可以推广到完整的非线性方程。
1. Introduction. This work concerns orbits of the restricted three-body problem; for a discussion of that problem the reader is referred to [2],[3, Chap. 6], and [4]. The specific interest here is the behavior of orbits near those three critical points correspondingto the collinear Lagrangian points and particularly those orbits whose Jacobi constant is just above that of the critical point. The Hill’s region corresponding to such values of the Jacobi constant contains a" neck" about the Lagrangian point; thus, in the case of the Lagrangian point between the mass points, orbits on the integral surface can make a transit (through the neck) from one mass point to the other. The aim here is to describe how orbitsin the" neck" look. The purpose for the work is twofold. First, in [5] a general Hamiltonian system (with two degrees of freedom) which admits an unstable critical point is considered, and the ultimate behavior or orbits with respect to the critical point is described in terms of certain disk mappings. In this work the way the disk construction appears in the restricted problem is described so that the results of [5] can be interpreted for this problem. The second purpose is to outline a scheme for designing low-energy earth-moon orbits. Numerical work on this problem has been initiated and will be described in a later paper; for the present only the general scheme is described (4).In order to get a good idea of the appearance of orbits in the" neck," which will be called the equilibrium region from now on, it is sufficient to discuss the equations of motion linearized near the critical point. Indeed, by virtue of J. Moser’s generalization of a theorem of A. Liapounoff (see [6]) all the qualitative results of such a discussion carry over to the full nonlinear equations.