Modified Delaunay Variables

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

Definition

A set of canonical variables redefined from standard Delaunay variables to avoid singularities when eccentricity approaches zero. Defined as Λ = L, P = L - G, Q = G - H, with corresponding angle variables λ, p, q. Modified Delaunay variables are particularly useful for analyzing mean motion resonances of low-eccentricity orbits and serve as the foundation for deriving MMR normal Hamiltonians.

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

  • Ding et al., 2025 — Cislunar Space Situational Awareness via Earth-Moon Resonant Orbits
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Contributors: ouyangjiahong, Ou Yang Jiahong