Lindstedt-Poincaré Method

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A semi-analytical series expansion method that constructs formal series solutions of periodic and quasi-periodic orbits and their manifolds in terms of amplitudes and phases. It incorporates high-order nonlinear terms of the equations of motion, achieving expansions up to order 25 or higher that provide initial conditions without further refinement. The expansions correspond to solutions of the Birkhoff normal form equations.

Application Value

This orbit type can serve as a transfer station in the cislunar transportation network or as a target orbit for missions. The manifold structure enables low-energy transfer trajectory design, reducing dependence on propellant. This representation facilitates analysis of periodic orbit family structures and bifurcation characteristics.

References

  • Masdemont - 2005 - High order expansions of invariant manifolds of libration point orbits with applications to mission design
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Contributors: ouyangjiahong, Ou Yang Jiahong