A new and better method based on Magnus integrator for hill's equations

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 Hill's 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.