论文标题
延续期间，周期性轨道家族靠近小行星的收敛
Convergence of a Periodic Orbit Family Close to Asteroids During a Continuation
论文作者
论文摘要
在这项工作中，我们研究了相对较大的周期性轨道的延续，并在某些条件下发现了收敛的存在，这在小行星研究中具有很大的意义，并且可以从全球角度从全球的角度理解动态特征的演变。基于多面体模型，通过一系列理论分析和推导得出收敛性，这表明周期性轨道将演变为具有正常周期比（例如2：1、3：3：2和4：3）的几乎圆形轨道，在适当的情况下几乎零扭转。作为此处开发的结果的应用，研究了三个小行星，（216）kleopatra，（22）kalliope和（433）爱神，并检测到几个代表性的周期性轨道家族，在三种不同的情况下会收敛：双向，导向和减少指导延续。同时，结论了这些数值示例中的四个共同点。首先，在单个周期轨道家族的周期性比例变化期间，（伪）切线分叉在尖端出现。此外，这些尖端的周期性比率与平均半径，最大扭转和最大曲率半径的变化中的转折点一致。此外，雅各布式常数总体上增加（或减少）的周期性比率增加（或减小）。我们发现周期比与雅各布常数之间的关系。结果表明，固定谐振状态的周期性比率具有最大效果和至上。最后，如果周期性轨道收敛到一个点，则可以是小行星的不稳定平衡点。
In this work, we study the continuation of a periodic orbit on a relatively large scale and discover the existence of convergence under certain conditions, which has profound significance in research on asteroids and can provide a total geometric perspective to understanding the evolution of the dynamic characteristics from a global perspective. Based on the polyhedron model, convergence is derived via a series of theoretical analyses and derivations, which shows that a periodic orbit will evolve into a nearly circular orbit with a normal periodic ratio (e.g., 2:1, 3:2, and 4:3) and almost zero torsion under proper circumstances. As an application of the results developed here, three asteroids, (216) Kleopatra, (22) Kalliope and (433) Eros, are studied, and several representative periodic orbit families are detected, with convergence in three different cases: bidirectional, increasing-directional and decreasing-directional continuation. At the same time, four commonalities among these numerical examples are concluded. First, a (pseudo) tangent bifurcation arises at the cuspidal points during the variations in the periodic ratios in a single periodic orbit family. In addition, these cuspidal points in the periodic ratio coincide with the turning points during the variations in the average radius, the maximal torsion and the maximal radius of curvature. Furthermore, the periodic ratio increases (or decreases) with an increase (or decrease) in the Jacobian constant overall. We find the relationship between periodic ratio and Jacobian constant. The results implies that the periodic ratios for a fixed resonant status have an infimum and a supremum. Finally, if the periodic orbit converges to a point, it can be an unstable equilibrium point of the asteroid.
