Gauss-Jackson积分器算法分析与验证  

Analysis and Validation of Gauss-Jackson Integral Algorithm

作　　者：罗志才[1,2] 周浩[1] 钟波[1,2] 张坤[1] 

机构地区：[1]武汉大学测绘学院,武汉市珞喻路129号430079 [2]武汉大学地球空间环境与大地测量教育部重点实验室,武汉市珞喻路129号430079

出　　处：《武汉大学学报（信息科学版）》2013年第11期1364-1368,共5页Geomatics and Information Science of Wuhan University

基　　金：国家自然科学基金资助项目(41131067;41174020;41104014);地理信息工程国家重点实验室开放基金资助项目(SKLGIE2013-M-1-3)

摘　　要：针对卫星轨道数值积分、变分方程解算等问题,研究了Gauss-Jackson积分器的原理和计算流程,提出了移位重排方式来优化其存储方式的方法,采用开普勒轨道、庞加莱轨道根数、状态转移矩阵等多种参数评估其性能,并与Runge-Kutta、Adams-Cowell等数值积分器进行了比较。计算结果表明,由于对启动点引入中值改正,Gauss-Jackson数值积分器的计算精度高、速度快,可为卫星轨道数值积分和变分方程求解等问题提供稳定、高效的算法。A numerical integrator plays an important role in satellite orbit integration and var- iational equation computation. After studying the principles and calculation methods used in the Gauss-Jackson integrator, we introduce a shift rearrangement method to improve its memory system. The performance of the improved algorithm was assessed with several pa- rameters, the Kepler orbit, Poincare elements, and state transition matrix. When compared with the Runge-Kutta and Adams-Cowell integrators, the improved Gauss-Jackson integrator with mid-corrector equations for the start point is more accurate and efficient, which means that it can meet the needs for satellite orbit integration and variational equation computation.

关 键 词：Gauss-Jackson积分器 多步法 卫星轨道数值积分 变分方程 

分 类 号：P228.41[天文地球—大地测量学与测量工程]