限制性四体问题中的时间相关不变流形

Time-Dependent Invariant Manifolds in the Restricted Four-Body Problem

借助有限时间Lyapunov指数(FTLE)定义了拉格朗日拟序结构(LCS),并将LCS作为不变流形的替代物。针对日-地-月双圆模型(BCM),利用LCS研究了限制性四体问题(R4BP)中的时间相关不变流形(TDIM)的性质。采用数值方法验证了TDIM是运动分界面和轨道不变集。继而,利用二分法对给定Poincare截面上的LCS进行了精确提取,通过一系列等能量面上的LCS描绘出TDIM在给定截面上的构形。最后,借助TDIM,初步研究了低能奔月轨道在非自治系统BCM中的直接构建。

The lagrangian coherent structure （LCS） is defined as ridges of finite-time Lyapunov exponent （FTLE） fields, and it is demonstrated that an understanding of time-dependent invariant manifold （TDIM） can be obtained by use of LCS. Taking Sun-Earth-Moon bicircular model （BCM） as an example and LCS as a tool, the property of the TDIM of restricted 4-body problem （R4BP） is demonstrated numerically that TDIM is invariant set of orbits and acts as separatrix. Dichotomy is then used to extract the LCS on the Poincare section, and the configuration of TDIM on specified section is illustrated by a series of LCS with regularly spaced energy. Finally, low energy transfer from the Earth to the Moon is constructed in BCM directly.