共线平动点中心流形上的轨道转移问题
doi: 10.11728/cjss2024.03.2023-0098 cstr: 32142.14.cjss2024.03.2023-0098
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杨富涛 男, 1999年11月出生于四川省宜宾市, 毕业于南京航空航天大学航天学院, 硕士研究生, 主要从事深空探测轨道动力学以及飞行器控制等方面的研究. E-mail: tt18284863524@163.com -
张汉清 男, 1980年11月出生于河南省开封市, 现为南京航空航天大学航天学院讲师, 硕士生导师, 主要从事深空探测轨道动力学等方面的研究. 本文通信作者. E-mail: hanqing@nuaa.edu.cn
作者简介:
Orbital Transfer Problem on the Central Manifold of Libration Points
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摘要: 圆形限制性三体问题共线平动点附近的平动点轨道由于其独特的动力学特性, 在深空探测任务中有着重要价值, 这些轨道间的轨道转移问题值得进行系统性研究. 针对平动点轨道的计算与延拓, 提出了一种基于数值的系统性计算平动点轨道的方法以及状态伴随法的轨道稳定维持策略. 在此基础上, 通过对大量平动点轨道不变流形以及平动点相空间中心流形的研究, 设计了一套通过脉冲机动实现平动点轨道间轨道转移的系统性解决方案. 该方法充分利用平动点动力学特性, 在仿真验证中证实了方案的有效性, 为平动点轨道转移研究提供了新的思路.Abstract: The Circular Restricted Three-body Problem (CR3BP) exhibits highly complex nonlinear dynamical characteristics in the vicinity of its libration points. The various periodic and quasi-periodic orbits within this region hold significant value for increasingly complex deep space exploration missions, offering more possibilities and flexibility in the design and control of mission trajectories. The issue of orbit transfers between these libration points warrants systematic investigation. To compute orbits around libration points, a numerical computation method based on escape time is proposed, enabling the unified calculation of various quasi-periodic orbits across a broad range of energy levels. Based on the manifold configuration of libration point orbit state points, a universal orbit maintenance strategy called state-adjoint techniques is proposed, yielding schemes that can sustain long-term stable operation of various libration point orbits. Building on extensive studies of invariant manifolds and Poincaré sections associated with numerous libration point orbits, a comprehensive solution has been designed to enable orbit transfers between libration points through pulse maneuvers. This method fully leverages the dynamical features of libration points and has been proven effective through simulation validation, offering new insights for research on libration point orbit transfers.
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图 2 稳定流形(实线)与不稳定流形(虚线)曲线
Figure 2. Stable (solid line) and unstable (dotted line) manifold plots
图 4 选取数据点稳定流形(实线)与不稳定流形(虚线)参数
Figure 4. Diagram of stable manifold (solid line) and unstable manifold (dotted line) parameters
图 6 空间中对称点稳定流形(实线)与不稳定流形(虚线)参数
Figure 6. Stable (solid line) and unstable manifold (dotted line) parameters at symmetrical points in space
图 17 地月系统L2点南北晕轨道转移
Figure 17. Orbital transfer between the north-halo and south-halo orbits at L2 points of the Earth-Moon system
图 18 地月系统L1点同族晕轨道转移
Figure 18. Orbital transfer between the halo orbital family at L1 points of the Earth-Moon system
表 1 平动点轨道初始状态与校正k值
Table 1. Initial state of the translational point track with corrected k-value
初始状态 (x0, y0, z0, α, β)=(0.84, 0.02, 0, 2.92, 1.17)
δ=0.00005校正次数 k 校正次数 k 1 –1.017×10–10 8 –4.62×10–11 2 –3.447×10–9 9 1.142×10–7 3 1.783×10–7 10 –2.903×10–6 4 –4.545×10–9 11 3.615×10–11 5 2.158×10–7 12 –8.679×10–8 6 4.728×10–8 13 2.455×10–6 7 –1.281×10–6 14 1.988×10–8 
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表 2 南北晕轨道转移参数
Table 2. Orbital transfer parameter between the north-halo and south-halo orbits
转移参数 转移时间/d 总Δv /(m⋅s–1) 文献数据 39.06 488.342 直接转移 0 427.325 间接转移 20.87 569.808
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表 3 同族晕轨道间转移参数
Table 3. Orbital transfer parameter between the halo orbital family
转移参数 转移时间/d 总Δv /(m⋅s–1) 文献数据 7.3048 882.766 间接转移 26.7843 545.899
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