Birkhoff Equations

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A reformulation of the circular restricted three-body problem that replaces six state variables with five new ones (x, y, z, γ, νz), eliminating velocity magnitude via the Jacobi integral. In the 3D Birkhoff equations, γ is the velocity azimuth angle and νz is the velocity component perpendicular to the x-y plane. This equation set has a concise form convenient for numerical integration and manifold computation.

Application Value

Based on its definition, a reformulation of the circular restricted three-body problem that replaces six state variables with five new ones (x, y, z, γ, νz), eliminating velocity magnitude via the jacobi integral. in the 3d b.

  • 三体问题（Three-Body Problem）
  • 最优控制（Optimal Control）
  • 轨迹优化（Trajectory Optimization）

References

  • Lunar capture trajectories and homoclinic connections through isomorphic mapping (Giancotti et al., 2012)
  • Pontani和Teofilatto - 2016 - Polyhedral representation of invariant manifolds applied to orbit transfers in the Earth–moon system
Improve this page
Last Updated:
Contributors: ouyangjiahong, Ou Yang Jiahong