Abstract This work presents a high-order perturbation expansion method for solving Lambert’s problem. The necessary condition for the problem is defined by a fourth-order Taylor expansion of the terminal error vector. The Taylor expansion partial derivative models are generated by Computational Differentiation (CD) tools. A novel derivative enhanced numerical integration algorithm is presented for computing nonlinear state transition tensors, where only the equation of motion is coded. A high-order successive approximation algorithm is presented for inverting the problems nonlinear necessary condition. Closed-form expressions are obtained for the first, second,third, and fourth order perturbation expansion coefficients. Numerical results are presented that compare the convergence rate and accuracy of first-through fourth-order expansions. The initial p-iteration starting guess is used as the Lambert’s algorithm initial condition. Numerical experiments demonstrate that accelerated convergence is achieved for the second-, third-, and fourth-order expansions, when compared to a classical first-order Newton method.
Higher Order Algorithm for Solving Lambert’s Problem
The Journal of the Astronautical Sciences ; 65 , 4 ; 400-422
2018-10-30
23 pages
Article (Journal)
Electronic Resource
English
Higher Order Algorithm for Solving Lambert’s Problem
Online Contents | 2018
|Wiley | 2021
|AIAA | 1976
|AIAA | 2016
|Online Contents | 2016
|