Polyhedral Representation

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A method representing state components on invariant manifolds as piecewise linear functions of two parameters: the injection point time and the manifold time of flight. By dividing the parameter plane into a rectangular grid and using four triangles for linear interpolation within each rectangle, rapid computation of state quantities is achieved. This representation is geometrically intuitive, simple to implement, and achieves engineering-adequate accuracy (92%~93% of regions with error less than 5m/s), applicable to trajectory optimization and rendezvous problems.

Application Value

In orbit design and optimization, this concept is used to analyze spacecraft motion characteristics in the cislunar multi-body gravitational field, providing a theoretical basis for low-energy transfer trajectory design.

  • Lorillo Stability Criterion
  • Stable Eigenvector
  • Lunar Fly-by Method
  • Reachability Set

References

  • Pontani和Teofilatto - 2016 - Polyhedral representation of invariant manifolds applied to orbit transfers in the Earth–moon system
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Contributors: ouyangjiahong, Ou Yang Jiahong