Celestial Mechanics and Dynamical Astronomy

, Volume 102, Issue 1–3, pp 149–162 | Cite as

Quaternions for regularizing Celestial Mechanics: the right way

  • Jörg Waldvogel
Original Article


Quaternions have been found to be the ideal tool for describing and developing the theory of spatial regularization in Celestial Mechanics. This article corroborates the above statement. Beginning with a summary of quaternion algebra, we will describe the regularization procedure and its consequences in an elegant way. Also, an alternative derivation of the theory of Kepler motion based on regularization will be given. Furthermore, we will consider the regularization of the spatial restricted three-body problem, i.e. the spatial generalization of the Birkhoff transformation. Finally, the perturbed Kepler motion will be described in terms of regularized variables.


Quaternions Regularization Kustaanheimo–Stiefel transformation Kepler formulas Birkhoff transformation Perturbed Kepler problem Joukowsky-Birkhoff mapping Quaternion algebra 


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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Swiss Federal Institute of Technology ETHZurichSwitzerland

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