椭圆型月球冻结轨道星座：基于环面的设计与分析
Elliptical Lunar Frozen Orbit Constellations: Torus-Based Design and Analysis
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中文总结 AI 辅助
本研究针对月球南极探测需求，开发基于环面的频域框架，结合FDDC、傅里叶代理重优化等技术，实现椭圆型月球冻结轨道星座的高效设计与高保真分析。
中文摘要 AI 辅助
椭圆型月球冻结轨道（ELFOs）是支持月球南极探测的月球卫星星座的理想候选。在现有基于频率的轨道分析方法基础上，本研究开发了一种基于环面的频域框架，用于星座级ELFO的设计与分析。在双平均动力学模型中，每个ELFO由三对频率-角度表征；对逐步提升保真度的模型进行系统比较，可识别出每一级引入的额外频率分量。角度参数化具有多种对称性，可大幅缩减设计空间，实现对星座构型的快速、无历元全局勘测。随后的高保真度细化与分析层结合了三部分：（1）频域微分校正器（FDDC），用于靶向期望的频率特性并抑制不期望的长周期振荡；（2）用于卫星间相位调整的傅里叶代理重优化，无需在循环中进行传播；（3）频谱归因，将可设计优化的覆盖损失与动力学固有损失分离。这些元素共同构成了用于ELFO星座设计与分析的保真度桥接与诊断框架。
英文摘要
Elliptical Lunar Frozen Orbits (ELFOs) are attractive candidates for lunar satellite constellations supporting lunar south pole exploration. Building on prior frequency-based orbit analysis methods, this investigation develops a torus-based, frequency-domain framework for constellation-level ELFO design and analysis. Within a doubly-averaged dynamical model, each ELFO is characterized by three frequency-angle pairs; a systematic comparison across progressively higher-fidelity models identifies the additional frequency components introduced at each level. The angular parametrization admits multiple symmetries that substantially reduce the design space, enabling a rapid, epoch-free global survey of constellation configurations. A higher-fidelity refinement and analysis layer then combines a (1) Frequency-Domain Differential Corrector (FDDC) that targets desired frequency properties and suppresses undesired long-period oscillations, (2) Fourier surrogate re-optimization for inter-satellite phasing without propagation in the loop, and (3) spectral attribution that separates design-refinable coverage losses from those inherent to the dynamics. Together, these elements supply a fidelity-bridging and diagnostic framework for ELFO constellation design and analysis.
