论文标题
从巴比伦的月球观察到浮动乘数和Conley-Zehnder索引
From Babylonian lunar observations to Floquet multipliers and Conley-Zehnder Indices
论文作者
论文摘要
我们月亮的月球时期 - 地球的同伴 - 可以追溯到巴比伦人，直到公元前600年左右，主教会的时间为29.53天，反常主义者为27.55天，而多痛的月份为27.21天。在本文中，我们根据Floquet乘数和Conley来定义和计算这些时期，这是空间丘陵农历问题中平面周期性轨道的Zhhnder索引，这是空间循环限制的三个身体问题的极限情况。对于非常低的能量，我们能够在分析上证明Planar Direct（家庭$ G $）和逆行周期轨道（家庭$ F $）的存在，并确定其Conley-Zhhnder指数。为了获得更高的能量，通过对线性流量的数值近似，我们还研究了来自$ g $和$ f $的家庭分叉的其他平面和空间周期性轨道。此外，我们的框架为家庭提供了有组织的结构，尤其是查看它们如何相互联系。由于我们分析的解决方案具有实际感兴趣，因此我们的工作将三个主题联系起来：巴比伦农历时期，象征性的几何形状和太空任务设计。
The lunar periods of our moon -- the companion of the Earth -- which date back to the Babylonians until around 600 BCE, are 29.53 days for the synodic, 27.55 days for the anomalistic and 27.21 days for the draconitic month. In this paper we define and compute these periods in terms of Floquet multipliers and Conley--Zehnder indices for planar periodic orbits in the spatial Hill lunar problem, which is a limit case of the spatial circular restricted three body problem. For very low energies, we are able to prove analytically the existence of the families of planar direct (family $g$) and retrograde periodic orbits (family $f$) and to determine their Conley-Zehnder index. For higher energies, by numerical approximations to the linearized flow, we also study other families of planar and spatial periodic orbits bifurcating from the families $g$ and $f$. Moreover, our framework provide an organized structure for the families, especially to see how they are connected to each other. Since the solutions we analyze are of practical interest, our work connects three topics: Babylonian lunar periods, symplectic geometry, and space mission design.
