Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics
Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics
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作者：
Koon, WS;Lo, MW;Ross, SD
在本文中，我们将动力系统技术应用于平面圆形限制性三体问题中的异宿连接和共振跃迁问题。这些相关现象在诸如彗星和小行星的捕获以及诸如“起源号”探测任务等太空任务的轨道设计等主题中已经受到关注有一段时间了。本文的主要新技术成果是对成对的周期轨道之间存在异宿连接进行了数值演示：一个周期轨道围绕平动点L - 1，另一个围绕L - 2，且这两个周期轨道具有相同的能量。这一结果被应用于共振跃迁问题以及具有规定行程的有趣轨道的显式数值构建。本文所阐述的观点是，与L - 1和L - 2相关的不变流形结构以及上述异宿连接是基本工具，有助于理解整个太阳系中的动力通道以及“内部”和“外部”希尔区域之间的传输和其他共振现象。（C）2000美国物理学会。[S1054 - 1500(00)00402 - X]
In this paper we apply dynamical systems techniques to the problem of heteroclinic connections and resonance transitions in the planar circular restricted three-body problem. These related phenomena have been of concern for some time in topics such as the capture of comets and asteroids and with the design of trajectories for space missions such as the Genesis Discovery Mission. The main new technical result in this paper is the numerical demonstration of the existence of a heteroclinic connection between pairs of periodic orbits: one around the libration point L-1 and the other around L-2, with the two periodic orbits having the same energy. This result is applied to the resonance transition problem and to the explicit numerical construction of interesting orbits with prescribed itineraries. The point of view developed in this paper is that the invariant manifold structures associated to L-1 and L-2 as well as the aforementioned heteroclinic connection are fundamental tools that can aid in understanding dynamical channels throughout the solar system as well as transport between the "interior" and "exterior" Hill's regions and other resonant phenomena. (C) 2000 American Institute of Physics. [S1054-1500(00)00402-X].