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摘要:
针对从月球停泊轨道出发直接再入大气的月地转移轨道设计问题，提出了一种数值求解算法。该算法由初值设计和精确解求解两部分组成。首先，根据轨道设计的相应约束，采用伪状态理论，通过简单迭代求解高精度的初值。然后，考虑精确的动力学模型，通过数值积分计算真实轨道和状态转移矩阵，并利用微分修正方法搜索精确解。该算法通过设计高精度的初值，降低了月地转移轨道的设计难度。数值仿真表明：该算法求解效率高，具有良好的鲁棒性。
Abstract:A new solution algorithm for the design of Moon-to-Earth transfer orbit which leaves from the Moon parking orbit with direct atmospheric reentry and single impulse is presented in this paper. The algorithm is divided into two steps, designing the initial solution and searching the exact solution. First, according to the constraint conditions, the high-precision initial solution is generated by simple iteration using pseudostate theory. Then, the real orbit and state transition matrix are calculated by numerical integration in the real dynamic model, and the exact solution is found by the differential correction method. Because the initial solution with high accuracy is used, the difficulty of finding the solution for the design of Moon-to-Earth transfer orbit is greatly reduced. Numerical simulations indicate that the algorithm is of high efficiency and good robustness.
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图 3 月地转移轨道3D示意图
Figure 3. Three-dimensional illustration of Moon-to- Earth transfer orbit
图 4 月地转移轨道2D示意图
Figure 4. Two-dimensional illustration of Moon-to- Earth transfer orbit
图 5 一个轨道周期内变轨速度增量变化趋势
Figure 5. Track change velocity increment versus time in one orbit period
表 1 初值设计时伪状态位置误差迭代过程
Table 1. Iteration process of pseudostate position error during initial solution design
迭代次数 Δx/m Δy/m Δz/m 1 7101140 -8735400 -3641240 2 453967 101658 104456 3 1622.07 279.576 393.42 4 102.868 13.296 21.020 5 5.799 0.804 1.249 6 0.350 0.0425 0.069 
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表 2 精确解求解时再入点状态偏差迭代过程
Table 2. Iteration process of reentry point state error during exact solution search
迭代次数 ΔRe/m Δcos ie Δcos φe 1 413183 0.0112 0.0007 2 6385.410 0.0019 0.0015 3 321.208 0.00012 0 4 2.334 0 0
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表 3 月地转移轨道特征参数
Table 3. Characteristic parameters of Moon-to-Earth transfer orbit
编号 再入
方式转移
时间/d再入点速度/
(m·s-1)再入
航程/km1 升轨 3.689 10.985 4969 2 升轨 3.871 10.984 10378 3 降轨 3.334 10.987 32748 4 降轨 3.516 10.985 38124
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