Quaternions and the perturbed Kepler problem

  • Jörg WaldvogelEmail author


Quaternions, introduced by Hamilton (Philos. Mag. 25, 489–495, 1844) as a generalization of complex numbers, lead to a remarkably simple representation of the perturbed three-dimensional Kepler problem as a perturbed harmonic oscillator. The paper gives an overview of this technique, including an outlook to applications in perturbation theories.


Kustaanheimo–Stiefel regularization Quaternions Perturbed Kepler problem Birkhoff transformation 


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© Springer 2006

Authors and Affiliations

  1. 1.Seminar for Applied MathematicsSwiss Federal Institute of Technology ETHZurichSwitzerland

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