Spherical Control Variables

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A parameterization of the thrust vector using three scalars: magnitude T, azimuth angle α, and elevation angle β. In CRTBP low-thrust optimization, the spherical control u=[T, α, β]ᵀ is converted to Cartesian thrust components via the radial-transverse-normal (RSW) basis. This decouples thrust magnitude from direction: the magnitude bound is simple (0≤T≤T_max), and the steering angle trust-region scaling is independent. When the velocity vector becomes collinear with the position vector and the RSW frame degenerates, the formulation switches to Cartesian control variables.

Application Value

This concept is fundamental to cislunar orbital mechanics and mission analysis, providing essential theoretical support for trajectory design and operational planning.

  • Retrograde Motion
  • Absolute Phase Bias
  • Relative Attitude Quaternion
  • Radial-Tangential-Normal Coordinate System, RTN

References

  • Aziz et al. 2019, JGCD
Improve this page
Last Updated:
Contributors: ouyangjiahong, Ou Yang Jiahong