Physics – Classical Physics
Scientific paper
2003-01-10
J. Phys. A 36, 6963 (2003)
Physics
Classical Physics
Scientific paper
10.1088/0305-4470/36/25/305
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.
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