Aim. The introduction of the full paper reviews some relevant papers in the open literature, points out what we believe to be their shortcomings,and then proposes the numerical method mentioned in the title,which we believe is new and better than previous ones and which is explaind in sections 1 and 2. Their core consists of; "Based on Magnus integrator method,the Hills equations were reduced-order and numerically simulated for the rail errors of the satellite formation flying in Hamiltonian system. The second-order dynamic system was reformulated as a system of first-order and the frame of reference was transferred by introducing new state variables so that the canonical characteristic was inherited from the dynamic system. This method was designed for solving the above new first-order system equations, which provide simpler calculations and better accuracy than the traditional fourth-order Runge-Kutta method. "With the presented method,the rail errors problem of two radiuses is studied;the numerical results, presented in Figs 1, and their analysis show preliminarily that it can indieed give good computational accuracy and stability.%基于Magnus积分方法,针对Hamilton系统下卫星编队绕飞轨道误差问题,对二阶Hill's方程进行了降阶变换和数值模拟.通过引进新状态变量将二阶动力学系统表示为一阶动力学系统,从而保留了原二阶动力学系统的典则性质.采用Magnus积分方法求解一阶系统方程,与传统四阶Runge -Kutta方法相比,该方法计算简单,精度高.文中采用该方法分析了两种绕飞半径的轨道误差问题,分析结果表明该方法具有良好的精度和稳定性.
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