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针对卫星轨道微分方程组的数值解法,提出了一种基于Richardson外推思想的定步长Adams-Cowell积分方法,分别对Adams方法和Cowell方法的PECE格式进行外推改进。结合外推改进的详细理论推导,总结出了不同阶积分公式的系数的数学规律,并以表格的形式给出,方便了工程实践。最后,利用卫星轨道二体运动方程对8阶改进的方法进行了仿真分析,由仿真结果可知,和未改进的算法相比,改进后的算法计算精度有了明显改进,在某些特定积分步长下的计算精度能提高一个数量级,证明了改进算法的有效性,此8阶改进的方法可用于工程实践。
Aiming at the numerical solution of satellite orbital differential equations, a fixed step Adams-Cowell integral method based on Richardson extrapolation is proposed. The PECE format of Adams and Cowell methods are extrapolated respectively. Combined with extrapolation to improve the detailed theoretical derivation, summed up the mathematical rules of the coefficients of different order integral formulas, and given in tabular form, to facilitate the engineering practice. Finally, using the satellite orbital motion equations to simulate the eight-step improvement, the simulation results show that compared with the unmodified algorithm, the accuracy of the improved algorithm has been significantly improved. In some specific integration steps The accuracy of this algorithm can be improved by one order of magnitude, which proves the effectiveness of the improved algorithm. The eight-step improvement method can be used in engineering practice.