The Journal of the Astronautical Sciences

, Volume 65, Issue 4, pp 400–422 | Cite as

Higher Order Algorithm for Solving Lambert’s Problem

  • Mohammad Alhulayil
  • Ahmad Bani Younes
  • James D. Turner


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.


Lambert’s problem Computational differentiation p-iteration 


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Copyright information

© American Astronautical Society 2018

Authors and Affiliations

  1. 1.Aerospace Engineering DepartmentKhalifa UniversityAbu DhabiUAE
  2. 2.Department of Aerospace EngineeringSan Diego State UniversitySan DiegoUSA
  3. 3.ManchesterUK

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