初值约束与两点边值约束轨道动力学方程的快速数值计算方法

It is a fundamental problem to efficiently solve the orbit dynamic systems occurred in the process of orbit design, space capture, deep space exploration and many other aerospace engineering missions. The traditional numerical integration methods, which are based on finite difference method, can hardly meet the requirement of low-latency computation in aerospace missions for their strict needs of small integration step size. In this paper, the high performance local collocation feedback iteration (LCFI) method is presented for orbit dynamic functions with initial value and two-point boundary-value constraints. LCFI does not need to estimate Jacobian matrix during the calculation process for that it is based on Picard iteration method, and it is able to save convergence time via combining error-feedback strategy. Besides, time domain collocation method is used to transfer the symbolic operations into algebraic operations, thus make the iterative formula of LCFI concise. In addition, LCFI is able to solve Lambert's problem efficiently via combining quasi linearization method and superposition method, and its parameters can be adaptively adjusted via an adopted ph mesh refinement method to better play its ability of calculating with large step size. The validity of LCFI is verified via solving the orbit propagation problem, the perturbed Lambert's problem, and the transfer trajectory in the circular restricted three-body model. Simulation results show that the computational efficiency of LCFI is higher than 1.5 times that of quasi linearization local variational iteration method, and the parameter adjustment method based on ph mesh refinement method is able to further increase the calculation speed of LCFI by more than 6 times.