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

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.