Birkhoff Normal Form

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

Definition

Normal form expansion of a Hamiltonian system near an equilibrium point or periodic orbit. Through successive reduction in the nearly integrable subspace, it can be used to prove existence and stability of periodic orbits.

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

  • Celletti - 2010 - Stability and chaos in celestial mechanics
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Contributors: ouyangjiahong, Ou Yang Jiahong