本文对受限制层级三体问题的渐进演化开展了解析分析，重点研究Kozai-Lidov（古在-里多夫）循环的相关条件——该循环中八极（三阶）项会引发轨道从顺行到逆行的翻转，且伴随极高的轨道偏心率。我们重新考察了Katz、Dong与Malhotra（发表于《Phys. Rev. Lett. 107, 181101 (2011)》）提出的方法，结果表明对于绝大多数初始条件，该解析推导可大幅简化，在极佳近似下可简化为单摆模型，进而得到显式的翻转判据。所得翻转判据远早于先前的判据，但在相空间的小部分区域内仍需使用原有判据。我们指出了早期推导中存在的一处逻辑错误，但阐明了该错误为何不会影响最终结果。
英文摘要：
The gradual evolution of the restricted hierarchical three body problem is analyzed analytically, focusing on conditions of Kozai-Lidov Cycles that may lead to orbital flips from prograde to retrograde motion due to the octupole (third order) term which are associated with extremely high eccentricities. We revisit the approach described by Katz, Dong and Malhotra (\href{https://doi.org/10.1103/PhysRevLett.107.181101}{Phys. Rev. Lett. 107, 181101 (2011)}) and show that for most initial conditions, to an excellent approximation, the analytic derivation can be greatly simplified and reduces to a simple pendulum model allowing an explicit flip criterion. The resulting flip criterion is much simpler than the previous one but the latter is still needed in a small fraction of phase space. We identify a logical error in the earlier derivation but clarify why it does not affect the final results.
Stability of hierarchical triples comprising a central massive body and a tight binary: the effect of inner and outer eccentricities on the binary breakup condition
Large-scale chaos in restricted hierarchical triples driven by short-range forces
School of Astronomy and Space Science, Nanjing University（南京大学天文与空间科学学院）；Key Laboratory of Modern Astronomy and Astrophysics in Ministry of Education, Nanjing University（南京大学现代天文与天体物理教育部重点实验室）
Predicting the Stability of Hierarchical Triple Systems with Convolutional Neural Networks
Okinawa Institute of Science and Technology（冲绳科学技术大学院大学）；Research Center for the Early Universe, School of Science, The University of Tokyo（东京大学理学部早期宇宙研究中心）
