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基于数值延拓的日月综合借力DRO入轨策略

张晨

张晨. 基于数值延拓的日月综合借力DRO入轨策略[J]. 北京航空航天大学学报,2024,50(4):1176-1186 doi: 10.13700/j.bh.1001-5965.2022.0494
引用本文: 张晨. 基于数值延拓的日月综合借力DRO入轨策略[J]. 北京航空航天大学学报,2024,50(4):1176-1186 doi: 10.13700/j.bh.1001-5965.2022.0494
ZHANG C. Low-energy transfer from Earth into DRO with hybrid gravity assist and numerical continuation[J]. Journal of Beijing University of Aeronautics and Astronautics,2024,50(4):1176-1186 (in Chinese) doi: 10.13700/j.bh.1001-5965.2022.0494
Citation: ZHANG C. Low-energy transfer from Earth into DRO with hybrid gravity assist and numerical continuation[J]. Journal of Beijing University of Aeronautics and Astronautics,2024,50(4):1176-1186 (in Chinese) doi: 10.13700/j.bh.1001-5965.2022.0494

基于数值延拓的日月综合借力DRO入轨策略

doi: 10.13700/j.bh.1001-5965.2022.0494
基金项目: 中国科学院空间科学战略性先导科技专项(XDA30040400);航天飞行动力学国家级重点实验室基金(6142210200302);中国科学院青促会创新人才项目(292022000030)
详细信息
    通讯作者:

    E-mail:chenzhang@csu.ac.cn

  • 中图分类号: V412.41

Low-energy transfer from Earth into DRO with hybrid gravity assist and numerical continuation

Funds: Strategic Priority Research Program on Space Science, the Chinese Academy of Sciences (XDA30040400); Foundation of State Key Laboratory of Space Flight Dynamics Lab (6142210200302); Youth Innovation Promotion Association, Chinese Academy of Sciences (292022000030)
More Information
  • 摘要:

    远距离逆行轨道(DRO)是地月空间中的一类周期轨道,这类轨道具有长期稳定、入轨能量低的特点,可作为未来载人月球和载人火星任务的中转站。对于地球至DRO的两脉冲入轨任务,采用日月综合借力(即同时使用弱稳定边界(WSB)和月球借力(LGA))可以最大化入轨质量,但是这类轨道对初值非常敏感。使用日月综合借力拓展DRO入轨脉冲包络,改进构造方法和提供解析梯度大幅提高多步打靶收敛率,提出2层伪弧长延拓方法进一步降低任务总脉冲。数值仿真采用共振比为2∶1的DRO,脉冲最低解采用“LGA+WSB+2LGA”的飞行模式,飞行时间为123天,近地轨道发射脉冲为3.125 km/s,DRO入轨脉冲仅为19.7 m/s。

     

  • 图 1  平面双圆限制性四体模型

    Figure 1.  Planar bicircular restricted four-body model

    图 2  地月系统DRO族

    Figure 2.  DRO family in Earth-Moon system

    图 3  WSB转移示意图(日地旋转系)

    Figure 3.  Schematic diagram of WSB transfer(Sun-Earth rotation system)

    图 4  “LGA+WSB+NLGA”的DRO入轨示意图

    Figure 4.  Schematic diagram of “LGA+WSB+NLGA” transfer from Earth into DRO

    图 5  月球轨道站支持的载人月球和火星任务示意图

    Figure 5.  Schematic diagram of cislunar orbital station supporting manned missions to the Moon and Mars

    图 6  多步打靶示意图

    Figure 6.  Schematic diagram of multiple shooting

    图 7  参数增量法延拓

    Figure 7.  Parametric incremental continuation

    图 8  伪弧长延拓

    Figure 8.  Pseudo-arc continuation

    图 9  多步打靶收敛解空间

    Figure 9.  Solution space of multiple shooting

    图 10  数值延拓后各区间轨道数的变化

    Figure 10.  Changes in number of orbits after numerical continuation

    图 11  数值延拓后的解空间

    Figure 11.  Solution space after numerical continuation

    图 12  第1层延拓和最优解

    Figure 12.  The first level continuation and optimal solution

    图 13  第2层延拓和最优解

    Figure 13.  The second level continuation and optimal solution

    图 14  伪弧长延拓的相空间变化轨迹

    Figure 14.  Phase space path with pseudo-arc continuation

    打靶约束的雅可比矩阵示意图

    Jacobian of constraints

    单轨道段变分示意图

    Variation of single track segment schematic diagram

    表  1  有限差分和解析梯度的对比

    Table  1.   Comparison between finite difference and analytical gradient

    名称 收敛数 收敛率/% 计算时间/s
    有限差分 309 8.44 18.01
    解析梯度 2361 64.54 20.24
    下载: 导出CSV

    表  2  数值延拓前后轨道对比

    Table  2.   Comparison of orbits before and after numerical continuation

    任务名称 延拓前 延拓后
    LEO发射时间/TU −31.944 945 682 3 −32.992 737 946 4
    DRO入轨时间/TU −4.422 676 457 9 −4.699 448 716 6
    LEO发射位置/LU [−0.025 926 418 9,
    −0.010 152 072 7]
    [−0.020 484 378 0,
    −0.014 946 105 5]
    LEO发射速度/VU [6.340 104 171 1,
    −8.603 190 754 6]
    [9.288 605 287 2,
    −5.179 229 375 6]
    DRO相位因子$\sigma $ 0.071 769 660 2 0.976 618 137 7
    LEO发射脉冲/(km·s−1 3.178 4 3.125 2
    DRO入轨脉冲/(km·s−1) 0.040 9 0.019 7
    任务总脉冲/(km·s−1) 3.219 4 3.144 9
    任务总时间/d 119.669 9 123.022 4
    下载: 导出CSV

    表  3  3种任务场景对比

    Table  3.   Comparison between 3 mission scenarios

    任务名称 发射脉冲/(km·s−1) 入轨脉冲/(km·s−1) 入轨质量/103 kg
    LEO至GEO 2.454 1.477 6.571
    LEO至LLO
    (综合借力)
    3.125 0.650 6.929
    LEO至DRO
    (综合借力)
    3.125 0.019 8.584
    下载: 导出CSV

    C1  数值仿真参数

    C1.   Numerical simulation parameters

    名称 数值
    太阳质量常数 μs/(km3·s−2) 132712440017.9870
    地球质量常数 μe/(km3·s−2) 398600.4328969392
    月球质量常数 μm/(km3·s−2) 4902.800582147764
    重力加速度 g0/(m·s−2) 9.80665
    地球平均半径 Re/km 6378.137
    月球平均半径 Rm/km 1738
    LEO地心距约束 r*leo/km 6578.137
    月球影响球半径 rsoi,m/km 66100
    归一化距离/LU 1
    归一化时间/TU 1
    归一化速度/VU 1
    归一化地月质量参数 μ 0.012151
    归一化太阳质量 ms 3.28901e5
    归一化太阳距离 ρs 388.811
    归一化太阳角速度 ωs −0.92519
    多步打靶离散点 n 20
    伪弧长延拓步长 Δs 0.1
    DRO入轨太阳相位角 θs(τN) [0,2π)
    DRO入轨相位因子 σ [0,1)
    DRO入轨脉冲模 ΔV/(m·s−1) [10,100]
    DRO入轨脉冲方向角 φ/rad [0,2π)
    2∶1共振DRO位置初值$r_{\mathrm{dro}}^0 $/LU [0.808936204186,0,]
    2∶1共振DRO速度初值$v_{\mathrm{dro}}^0 $/VU [0,0.515632164331]
     注:1 LU=384 400 km, 1 TU=4.348 113 05 d, 1 VU=1.023 232 81 km/s。
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-06-16
  • 录用日期:  2022-08-19
  • 网络出版日期:  2022-09-01
  • 整期出版日期:  2024-04-29

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