In mathematical physics, the Kustaanheimo–Stiefel regularization is a method to transform the spatial Kepler problem into a spatial harmonic oscillator using the Kustaanheimo–Stiefel (regularization) map. Both are named after Paul Kustaanheimo and Eduard Stiefel, who introduced them in 1965. Simply put, the idea is to increase the dimension to untangle singularities arising from collisions.
Kustaanheimo–Stiefel map The Kustaanheimo–Stiefel map is an extension of the complex Hopf fibration , using complex and complex projective space given by , by a squared radial component. It is a map given by filling with of the map:
In cartesian coordinates, the Kustaanheimo–Stiefel map is given by:Waldvogel 2010, Eq. (32)
The above squaring of the distance, hence a, follows from the binomial formulas.
See also
Levi-Civita regularization, analogous using the real Hopf fibration Moser regularization Ligon–Schaaf regularization
Literature
References