论文标题
分层三个身体问题的固定点
The Stationary Points of the Hierarchical Three Body Problem
论文作者
论文摘要
我们在行星极限（M_2，M_3 << m_1）中研究了二次和八极序列的层次三个身体问题的固定点。我们证明，八极顺序的延伸保留在小偏心率E_2的极限的极限上，但稳定固定点的新家族都发生在序列和逆行病例中。 最重要的新均衡是那些从四极溶液分支并扩展到大E_2的平衡。这些家族的Apsidal对齐是质量和内行星偏心率的函数，并取决于欧米茄_1和omega_2在四极级的相对方向。 这些新的平衡也是对相对论进动的不稳定影响最有弹性的。 我们发现其他平衡能够在径向轨道的极限中启用围绕中心的内部行星参数，并在共浮游极限中恢复Laplace-Lagrange解决方案的非线性类似物。最后，我们表明，用怪异的Kozai Lidov机制鉴定出的混乱扩散和轨道翻转及其变体可以从此处讨论的固定点来理解。
We study the stationary points of the hierarchical three body problem in the planetary limit (m_2, m_3 << m_1) at both the quadrupole and octupole orders. We demonstrate that the extension to octupole order preserves the principal stationary points of the quadrupole solution in the limit of small outer eccentricity e_2 but that new families of stable fixed points occur in both prograde and retrograde cases. The most important new equilibria are those that branch off from the quadrupolar solutions and extend to large e_2. The apsidal alignment of these families is a function of mass and inner planet eccentricity, and is determined by the relative directions of precession of omega_1 and omega_2 at the quadrupole level. These new equilibria are also the most resilient to the destabilizing effects of relativistic precession. We find additional equilibria that enable libration of the inner planet argument of pericentre in the limit of radial orbits and recover the non-linear analogue of the Laplace-Lagrange solutions in the coplanar limit. Finally, we show that the chaotic diffusion and orbital flips identified with the Eccentric Kozai Lidov mechanism and its variants can be understood in terms of the stationary points discussed here.
