高偏心率下的分层三体问题 = 简单摆 II：包含 Brown 哈密顿量的八极项
Hierarchical Three-Body Problem at High Eccentricities = Simple Pendulum II: Octupole including Brown's Hamiltonian
AI总结：
本文在高偏心率区域解析分析了分层限制性三体问题，证明 Brown 哈密顿量的效应等价于简单摆模型，并给出了明确的轨道翻转判据。
摘要：
本文在高偏心率区域解析分析了具有大质量摄动体的分层限制性三体问题的极长期演化。外轨道时间尺度上的摄动可以在长时间尺度上累积，并与八极项的影响相当。这些摄动由 Brown 哈密顿量描述——在文献中具有不同形式。我们证明，在高偏心率区域，Brown 哈密顿量的效应是偏心率矢量的方位角进动，并且可以解析求解。事实上，该动力学等价于一个简单摆模型，从而允许给出明确的翻转判据。
英文摘要：
The very long-term evolution of the hierarchical restricted three-body problem with a massive perturber is analyzed analytically in the high eccentricity regime. Perturbations on the time scale of the outer orbit can accumulate over long timescales and be comparable to the effect of the octupole term. These perturbations are described by Brown's Hamiltonian - having different forms in the literature. We show that at the high eccentricity regime - the effect of Brown's Hamiltonian is an azimuthal precesssion of the eccentricity vector and can be solved analytically. In fact, the dynamics are equivalent to a simple pendulum model allowing an explicit flip criterion.
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。
