Cylindrical Isomorphic Mapping

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A geometric transformation that maps the Birkhoff state (x, y, γ) to cylindrical coordinates (X, Y, Z) defined by X = x - xL1, Y = ρcosγ, Z = ρsinγ (ρ = y - ymin). Under this mapping, the stable and unstable invariant manifolds of a libration-point periodic orbit appear as tube-shaped structures emanating from the transformed periodic orbit, revealing topological features and intersections that govern chaotic dynamics in the three-body problem.

Application Value

In orbital design, analysis, and control, dynamics models are used to predict spacecraft trajectories, with equations of motion solved numerically or analytically. This concept underpins critical mission capabilities including orbital maneuver design, orbit improvement, and formation flying.

References

  • Lunar capture trajectories and homoclinic connections through isomorphic mapping (Giancotti et al., 2012)
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Contributors: ouyangjiahong, Ou Yang Jiahong