交换轨道--共轨运动的一个有趣例子
Exchange orbits - an interesting case of co-orbital motion
摘要：
本文讨论了两个天体在1：1平均运动共振中的一种特殊构型，即所谓的交换轨道。至少在理论上存在两种不同的类型：交换a轨道和交换e轨道。第一种情况是：两个天体围绕一个中心天体运行，它们在圆形轨道上的半长轴几乎相同。由于半长轴的差异相对较小，它们不时相遇并交换它们的半长轴。然后，内行星移动到另一个行星的外面，反之亦然。第二种情况是：两颗行星相对于半长轴在几乎相同的轨道上运动，一颗在圆形轨道上，另一颗在偏心轨道上。在它们的动力学演化过程中，它们改变了轨道的特性，圆形轨道变成椭圆形轨道，而椭圆形轨道变成圆形轨道。这个“游戏”会定期重复。在这项新的研究中，我们扩展的数值计算这两个交换轨道的三维情况下，并在另一个扩展处理的问题时，这些轨道被扰动的第四个机构。我们的结果在图表的形式显示相当不错，对于各种各样的初始条件，这两种配置是稳定的，并留在这个交换轨道。
英文摘要：
In this investigation we treat a special configuration of two celestial bodies in 1:1 mean motion resonance namely the so-called exchange orbits. There exist -- at least -- theoretically -- two different types: the exchange-a orbits and the exchange-e orbits. The first one is the following: two celestial bodies are in orbit around a central body with almost the same semi-major axes on circular orbits. Because of the relatively small differences in semi-major axes they meet from time to time and exchange their semi-major axes. The inner one then moves outside the other planet and vice versa. The second configuration one is the following: two planets are moving on nearly the same orbit with respect to the semi-major axes, one on a circular orbit and the other one on an eccentric one. During their dynamical evolution they change the characteristics of the orbit, the circular one becomes an elliptic one whereas the elliptic one changes its shape to a circle. This 'game' repeats periodically. In this new study we extend the numerical computations for both of these exchange orbits to the three dimensional case and in another extension treat also the problem when these orbits are perturbed from a fourth body. Our results in form of graphs show quite well that for a large variety of initial conditions both configurations are stable and stay in this exchange orbits.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
