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借助有限时间Lyapunov指数(FTLE)定义拉格朗日拟序结构(LCS),并以单摆系统为例阐述LCS与动力系统中不变流形之间的联系.利用LCS研究椭圆限制性三体问题(ER3BP)中的时间周期不变流形的性质.采用数值方法验证得到了两点结论:时间周期不变流形的内部是穿越轨道集,外部是非穿越轨道集;时间周期不变流形是轨道的不变集.
The Lagrangian Structure (LCS) is defined by means of the finite-time Lyapunov exponent (FTLE) and the relationship between LCS and invariant manifolds in dynamical systems is illustrated by taking the pendulum system as an example. Using LCS to study elliptic constrained trisomy The property of the time invariant manifold in the problem (ER3BP) is verified by numerical methods. Two conclusions are obtained by the numerical method: Time-invariant manifolds are traversing orbitals outside and non-transitive orbitals outside; time-invariant manifolds Is a constant set of orbits.