大范围收敛的摄动Lambert问题新型解法:拟线性化-局部变分迭代法

研究实时、高效、稳定性强的高性能空间轨道计算方法对于中国未来航天工程具有重大应用价值。针对强非线性系统的多维两点边值问题，提出了一种拟线性化-局部变分迭代法（QL-LVIM），通过拟线性化（QL）思想，将非线性两点边值问题转化为一系列具有一定迭代格式，并且成对出现的初值问题，进而通过局部变分迭代法（LVIM）对其进行求解。利用拟线性化的大范围收敛特性和局部变分迭代法的快收敛、高精度特性，该方法能够在较大的时间和空间尺度下快速精确获得摄动Lambert问题的初速度和转移轨道，其收敛域远大于传统的牛顿打靶法，为航天器轨道转移提供了一种简便高效、稳定性强的新型计算方法。在不同轨道情形下，与几类参考方法对比，结果表明本方法能够在计算效率方面实现大幅提升，并且能够在大范围内实现快速收敛。方法的有效性在地-月系三体问题中得到了进一步验证。

A novel quasi linearization-local variational iteration method with large convergence domain for solving perturbed Lambert's problem

Research on real-time, efficient, and stable orbit computational method has significant application value to China's future space engineering. A novel Quasi Linearization-Local Variational Iteration Method (QL-LVIM) for solving the multidimensional two-point boundary-value problems of strongly nonlinear systems is proposed. With the Quasi Linearization (QL) method, the nonlinear two-point boundary-value problem is transformed into a series of iterative initial value problems which appear in pairs. Then, these initial value problems are solved with the Local Variational Iteration Method (LVIM). Combining wide convergence of the Quasi Linearization method and rapid convergence and high precision of the Local Variational Iteration Method, the proposed algorithm can precisely and efficiently obtain the accurate initial velocity and transfer orbit of the perturbed Lambert's problem in large time and space scales. The convergence domain of the QL-LVIM is much wider than that of the traditional Newton's shooting method. It provides a convenient, efficient and stable algorithm for calculating the transfer orbit of spacecraft. Comparisons are made with several reference methods under different orbit circumstances. The results illustrate that the QL-LVIM can not only significantly improve the calculation efficiency, but also provide a much wider convergence domain. Validity of the proposed algorithm is further verified by solving a three-body problem in the Earth-Moon system.