Birkhoff Normal Form

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

Definition

A canonical transformation that simplifies the Hamiltonian near an equilibrium point to a form depending only on action variables, eliminating non-resonant terms. The Lindstedt-Poincaré series expansions correspond to formal series solutions of the Birkhoff normal form equations.

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

  • Alessi 等 - 2009 - Leaving the moon by means of invariant manifolds of libration point orbits
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Contributors: ouyangjiahong, Ou Yang Jiahong