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The Kustaanheimo–Stiefel transformation in geometric algebra

T Bartsch

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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.


PACS

45.50.Pk Celestial mechanics

02.10.-v Logic, set theory, and algebra

02.40.-k Geometry, differential geometry, and topology

MSC

70G55 Algebraic geometry methods

70F15 Celestial mechanics

Subjects

Mathematical physics

Astrophysics and astroparticles

Dates

Issue 25 (27 June 2003)

Received 13 January 2003, in final form 22 April 2003

Published 12 June 2003



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