Low-thrust trajectory design in the context of the three-body problem, particularly in the vicinity of liberation points, is addressed in this paper with a focus on efficiency and accuracy. The Finite Fourier series, previously successful in approximating near-coplanar low-thrust trajectories within two-body dynamics, is applied to the challenging landscape of the three-body problem, marked by instability and nonlinearity. This paper introduces a novel approach for constructing an initial guess trajectory, which combines coast arcs from periodic orbits and intermediate trajectory arcs from other natural dynamical structures. The resulting initial guess trajectory is instrumental in generating efficient initial estimates for the coefficients of the Finite Fourier series. The study encompasses the analysis of homoclinic and heteroclinic transfers in both two-dimensional and three-dimensional scenarios. The approximated trajectories derived from this methodology serve as invaluable starting points for high-fidelity optimization solvers, offering promise for enhancing the precision and efficiency of low-thrust transfers in cislunar space.

中文翻译：

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基于形状的地月空间周期轨道间低推力转移方法

本文讨论了三体问题背景下的低推力弹道设计，特别是在解放点附近，重点关注效率和准确性。有限傅立叶级数先前成功地逼近了二体动力学中的近共面低推力轨迹，现在被应用于具有挑战性的三体问题，其特点是不稳定性和非线性。本文介绍了一种构建初始猜测轨迹的新方法，该方法结合了周期性轨道的海岸弧和其他自然动力结构的中间轨迹弧。由此产生的初始猜测轨迹有助于生成有限傅立叶级数系数​​的有效初始估计。该研究包括二维和三维场景中同宿和异宿传输的分析。从这种方法得出的近似轨迹可以作为高保真优化求解器的宝贵起点，为提高地月空间中低推力传输的精度和效率提供了希望。