Kustaanheimo-Stiefel transformation ?

[astronomia84]

Kustaanheimo-Stiefel transformation

What is Kustaanheimo-Stiefel transformation (KS) & why is useful for restricted three-body problem ?

 

[Kaleb]

The Kustaanheimo-Stiefel (KS) transformation maps the non-linear and singular equations of motion of the three-dimensional Kepler problem to the linear and regular equations of a four-dimensional harmonic oscillator. It is used extensively in studies of the perturbed Kepler problem in celestial mechanics and atomic physics. In contrast to the conventional matrix-based approach, the formulation of the KS transformation in the language of geometric Clifford algebra offers the advantages of a clearer geometrical interpretation and greater computational simplicity. It is demonstrated that the geometric algebra formalism can readily be used to derive a Lagrangian and Hamiltonian description of the KS dynamics in arbitrary static electromagnetic fields. For orbits starting at the Coulomb centre, initial conditions are derived and a framework is set up that allows a discussion of the stability of these orbits.

Source: http://www.citebase.org/abstract?id=oai%3AarXiv.org%3Aphysics%2F0301017

 

[astronomia84]

Thanks for the link .

More specific information about KS & restricted three-body problem?