Abstract:
The Kustaanheimo–Stiefel transformation regularizes collision singularities in the spatial restricted three-body problem by lifting the dynamics to a higher-dimensional phase space. The resulting system has a constrained physical submanifold and a nontrivial geometry near collision. I will describe the regularized dynamics and focus on the KS origin, where the linearization undergoes a transition from hyperbolic to elliptic behavior as the Jacobi constant varies. In the elliptic regime, a 1:1:1:1 resonance appears. This motivates a normal-form analysis of the regularized system, with particular attention to the constraints defining the physical dynamics. Ongoing work with J. D. Mireles James and Luke Peterson.