The Kustaanheimo-Stiefel (KS) transformation is a mathematical technique that maps the non-linear equations of motion of the three-dimensional Kepler problem to the linear equations of a four-dimensional harmonic oscillator. This transformation is crucial for analyzing the restricted three-body problem in celestial mechanics and atomic physics. Utilizing geometric Clifford algebra for the KS transformation provides a clearer geometrical interpretation and simplifies computations compared to traditional matrix methods. The discussion also highlights the derivation of Lagrangian and Hamiltonian descriptions of KS dynamics in static electromagnetic fields, along with the establishment of initial conditions for orbits starting at the Coulomb center.
PREREQUISITESResearchers in celestial mechanics, physicists studying atomic interactions, and mathematicians interested in advanced algebraic techniques will benefit from this discussion on the Kustaanheimo-Stiefel transformation and its applications.
