优化包络面积法三角平动点短周期轨道设计与分析

刘勇; 范大伟; 刘磊; 李皓皓; 曹鹏飞

doi:10.7527/S1000-6893.2025.32708

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DOI: https://doi.org/10.7527/S1000-6893.2025.32708

优化包络面积法三角平动点短周期轨道设计与分析

刘勇 ,
范大伟 ,
刘磊 ,
李皓皓 ,
曹鹏飞

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1. 北京飞控
2. 北京航天飞行控制中心

收稿日期: 2025-08-26

修回日期: 2025-12-02

网络出版日期: 2025-12-08

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Design and Analysis of Short Period Orbits of Triangular Translation Points by Optimized Envelope Area Method

LIU Yong ,
FAN Da-Wei ,
LIU Lei ,
LI Hao-Hao ,
CAO Peng-Fei

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Received date: 2025-08-26

Revised date: 2025-12-02

Online published: 2025-12-08

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摘要

本文首先建立了圆型限制性三体动力学模型与高精度动力学模型，针对沿x方向轨道延拓能力较为有限的问题，提出了三角平动点短周期轨道的角度延拓法并求解出了更大范围的地月三角平动点短周期轨道族；针对摄动力影响下，三角平动点短周期轨道易于发散，不利于工程应用以及并行打靶法在计算多圈短周期轨道时计算量大，收敛性难以保证的问题，提出了高精度模型下三角平动点短周期轨道的优化包络面积法和混合法等高效计算方法；采用该方法对地月L4点的短周期轨道进行了分析，发现高精度模型下地月系短周期轨道包络近似于圆型限制性三体轨道但散布于包络内，以及不同历元计算的短周期轨道最终都稳定在一定范围内等特点，为三角平动点的实际应用打下了基础。

关键词： 圆型限制性三体问题; 三角平动点; 坐标延拓; 包络面积; 短周期轨道

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刘勇 , 范大伟 , 刘磊 , 李皓皓 , 曹鹏飞 . 优化包络面积法三角平动点短周期轨道设计与分析[J]. 航空学报, 0 : 1 -0 . DOI: 10.7527/S1000-6893.2025.32708

Abstract

This paper first establishes the circular restricted three-body dynamical model and a high-precision dynamical model. In response to the limited orbital extension capability along the x-direction, an angle extension method for short-period orbits of triangular libration points is proposed, which solves the family of larger-range lunar-Earth triangular libration points' short-period orbits. To address the issues where short-period orbits of triangular libration points are prone to divergence under the influence of perturbing forces, which is not conducive to engineering applications, and where the parallel shooting method has large computational loads and poor convergence when calculating multi-orbit short-period orbits, efficient calculation methods such as the optimized envelope area method and hybrid method for short-period orbits of triangular libration points under high-precision models are proposed. Using this method, an analysis of the short-period orbit at the lunar L4 point was conducted, revealing characteristics such as the envelope of short-period orbits in the lunar-Earth system under the high-precision model being approximately circular restricted three-body orbits but scattered within the envelope, and that short-period orbits calculated at different epochs ultimately stabilize within a certain range. These findings lay the foundation for the practical application of triangular libration points.

Key words： Circular restricted three-body problem; Triangular translation point; Coordinate continuation; Envelope area; Short-periodic orbit

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