The hierarchical triple-body approximation has useful applications to a variety of systems from planetary and stellar scales to supermassive black holes. In this approximation, the energy of each orbit is separately conserved, and therefore the two semimajor axes are constants. On timescales much larger than the orbital periods, the orbits exchange angular momentum, which leads to eccentricity and orientation (i.e., inclination) oscillations. The orbits' eccentricity can reach extreme values, leading to a nearly radial motion, which can further evolve into short orbit periods and merging binaries. Furthermore, the orbits' mutual inclinations may change dramatically from pure prograde to pure retrograde, leading to misalignment and a wide range of inclinations. This dynamical behavior is coined the “eccentric Kozai-Lidov mechanism.” The behavior of such a system is exciting, rich, and chaotic in nature. Furthermore, these dynamics are accessible from a large part of the triple-body parameter space and can ...

中文翻译：

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偏心 Kozai-Lidov 效应及其应用

分层三体近似对从行星和恒星尺度到超大质量黑洞的各种系统都有有用的应用。在这个近似中，每个轨道的能量是单独守恒的，因此两个半长轴是常数。在远大于轨道周期的时间尺度上，轨道交换角动量，这导致偏心率和方向（即倾角）振荡。轨道的偏心率可以达到极值，导致近乎径向的运动，这可以进一步演变成短轨道周期和合并双星。此外，轨道的相互倾角可能会发生巨大变化，从纯顺行变为纯逆行，导致错位和大范围的倾角。这种动态行为被称为“古怪的 Kozai-Lidov 机制”。”这样一个系统的行为本质上是令人兴奋的、丰富的、混乱的。此外，这些动力学可以从三体参数空间的很大一部分访问，并且可以......