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采用变分法推导得出指标函数的数值偏导数矩阵,进而构造出一种最速下降法,能快速确定燃料最优两脉冲火星交会机会。算例表明,该方法能从Pork-Chop的概略搜索结果出发,快速给出2015~2018年度的探测火星机会,其地球出发能量仅7.749 8 km2/s2,火星抵达速度为2.974 7 km/s,地火转移时间约208.6天。此外,最速下降法还可以作为一种通用的深空探测机会搜索与转移轨道设计方法,在金星、木星、土星等星际任务分析中发挥作用。
The variational method is used to derive the numerical partial derivative matrix of the index function, so as to construct a steepest descent method, which can quickly determine the optimal two-pulse Mars intersection. The example shows that this method can quickly give the exploration opportunity of Mars from 2015 to 2018 based on the results of Pork-Chop’s rough search. Its departure energy is only 7.749 8 km2 / s2 and its arrival rate is 2.974 7 km / s. Fire transfer time of about 208.6 days. In addition, the steepest descent method can also be used as a general search and transfer orbit design method for deep space exploration opportunities, and plays an important role in the analysis of interstellar missions such as Venus, Jupiter and Saturn.