任意倾角多层次三体系统的广义Hill稳定性准则
Generalized Hill-Stability Criteria for Hierarchical Three-Body Systems at Arbitrary Inclinations
摘要：
三体问题的一个基本方面是它的稳定性。大多数稳定性研究都集中在共面三体问题上，推导出这种正/逆系统的动力学稳定性的分析准则。倾斜系统的数值研究现象映射其稳定性区域，但既没有补充它的理论框架，也没有提供令人满意的适合他们的相互倾斜的依赖。本文提出了一种新的方法来研究具有任意倾角的多层次三体系统的稳定性，该方法不仅考虑了系统的瞬时稳定性，而且考虑了系统的长期稳定性以及通过Lidov-Kozai循环和矢量的演化.将Hill稳定性准则推广到任意倾斜的三元系，解释了拟稳定区的存在性，并刻画了其稳定性的倾斜依赖性。我们补充了广泛的数值研究的分析处理，以测试我们的分析结果。我们发现，良好的对应性高的倾斜度$(\sim120^{\circ}$），超过这一协议是边际。在如此高的倾角下，稳定半径更大，内外周期之间的比值变得相当，我们的长期平均方法不再严格有效。因此，我们结合我们的解析结果与多项式拟合的数值结果，得到一个广义的稳定性公式的三重系统在任意倾角。除了提供一个广义的世俗为基础的物理解释的非共面系统的稳定性，我们的研究结果有直接的影响，任何三重系统，特别是双行星和月球/卫星系统，我们简要讨论了后者作为我们的模型的测试案例。
英文摘要：
A fundamental aspect of the three-body problem is its stability. Most stability studies have focused on the co-planar three-body problem, deriving analytic criteria for the dynamical stability of such pro/retrograde systems. Numerical studies of inclined systems phenomenologically mapped their stability regions, but neither complement it by theoretical framework, nor provided satisfactory fit for their dependence on mutual inclinations. Here we present a novel approach to study the stability of hierarchical three-body systems at arbitrary inclinations, which accounts not only for the instantaneous stability of such systems, but also for the secular stability and evolution through Lidov-Kozai cycles and evection. We generalize the Hill-stability criteria to arbitrarily inclined triple systems, explain the existence of quasi-stable regimes and characterize the inclination dependence of their stability. We complement the analytic treatment with an extensive numerical study, to test our analytic results. We find excellent correspondence up to high inclinations $(\sim120^{\circ}$), beyond which the agreement is marginal. At such high inclinations the stability radius is larger, the ratio between the outer and inner periods becomes comparable, and our secular averaging approach is no longer strictly valid. We therefore combine our analytic results with polynomial fits to the numerical results to obtain a generalized stability formula for triple systems at arbitrary inclinations. Besides providing a generalized secular-based physical explanation for the stability of non co-planar systems, our results have direct implications for any triple systems, and in particular binary planets and moon/satellite systems; we briefly discuss the latter as a test case for our models.
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