An Adaptive Analytic Continuation Technique for the Computation of the Higher Order State Transition Tensors for the Perturbed Two-Body Problem

摘要

In this paper, the higher order State Transition Tensors are computed using the Analytic Continuation method. Analytic Continuation is a Taylor series based method applied to the fundamental orbit problem. Two scalar quantities, f and g_p, are defined and recursively differentiated using Leibniz product rule to obtain the higher order time derivatives that are used in to obtain the Taylor series expansion solution. The method has been shown to highly precise and computationally efficient in trajectory calculations. Recently, the first order State Transition Matrix (STM) has been developed using Analytic Continuation accounting for gravitational and atmospheric drag perturbations. Numerical simulations are shown for four types of orbits; LEO, MEO, GTO and HEO with J_2 perturbation for 10 orbit periods. First, the symplectic check is shown maintaining double precision accuracy for all types of orbits. Then, the higher order state transition tensors are applied to the error propagation of the state variables and results are compared with the results using first order STM. The results show three orde to increase the accuracy.