Indirect Methods

Author: Tianjiang Shuo Website: https://cislunarspace.cn

Definition

A class of trajectory optimization methods that derives first-order necessary conditions (co-state equations, Hamiltonian, etc.) via variational calculus and Pontryagin's maximum principle, then solves the resulting two-point boundary value problem via shooting methods. Indirect methods offer high accuracy and convergence order but are sensitive to initial guesses, with co-state initial values difficult to select.

Application Value

This concept plays a key role in trajectory transfer design, helping evaluate transfer costs and flight time to provide quantitative basis for mission trade studies. Combined with global search algorithms, multiple solution families and Pareto frontiers can be identified to guide orbital design decisions.

References

  • Vellutini & Avanzini, 2014, Shape-based design of low-thrust trajectories to cislunar lagrangian point
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Contributors: ouyangjiahong, Ou Yang Jiahong