A quasi-linear local variational iteration method for orbit transfer problems

A novel Quasi-linear Local Variational Iteration Method (QLVIM) for solving two-point boundary value problems (TPBVPs) of strongly nonlinear systems is proposed. With quasi-linearization technique, the multidimensional nonlinear TPBVP is transformed into a series of iterative linear TPBVPs, and then into initial value problems (IVPs) which appear in pairs. Then these IVPs are solved by Local Variational Iteration Method (LVIM). Combining the rapid convergence of quasi-linearization with the high computational efficiency of LVIM, the proposed QLVIM can solve various orbit transfer problems in aerospace engineering efficiently and accurately. The high-performance of this method is verified in solving perturbed Lambert's problems and a circular restricted three-body orbit transfer problem. Comparisons with various methods show that the QLVIM has the advantages of high convergence speed, low computation cost and longer solvable time span. Rather than a refined initial guess of starting velocity, the QLVIM only needs a rough initial guess of the trajectory. The results also prove that the QLVIM is capable of solving long-time-span orbit transfer problem. A theoretical proof of its quadratic convergence is given at last.