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Feedback-Accelerated Picard Iteration for Orbit Propagation and Lambert’s Problem

This paper presents a new Feedback-Accelerated Picard Iteration method for solving long-term orbit propagation problems and perturbed Lambert’s problems. This method is developed by combining the collocation method and the variational iteration method over large-time-steps. The resulting iterative formulae are explicitly derived so that they can be directly adopted to solve problems in orbital mechanics. Several typical orbit regimes incorporating high-order gravity and air drag force are used to demonstrate the application of the proposed method in orbit propagation. Further, the Feedback-Accelerated Picard Iteration method is used to solve perturbed orbit transfer problems. The combination of it with a Fish-Scales-Growing Method successfully extends its convergence domain and provides a potential approach for solving long duration two-point boundary value problems in conservative systems. The numerical results show that the proposed method is highly precise and efficient.

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