Kustaanheimo-Stiefel Transformation

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A regularization transformation for collision singularities in the spatial three-body problem, mapping points in four-dimensional space to three-dimensional space while preserving Hamiltonian structure. An extension of the Levi-Civita transformation to spatial problems.

Application Value

Kustaanheimo-Stiefel Transformation plays an important role in orbital dynamics and attitude control, serving as a critical tool for analyzing spacecraft motion characteristics. Research on this concept enables optimization of orbit transfer schemes and improvement of control system performance.

Related Concepts

• Restricted Three-Body Problem
• KAM Theorem
• Hill Clohessy Wiltshire Equations
• State Transition Function

References

• Celletti - 2010 - Stability and chaos in celestial mechanics.