Regular and Chaotic Dynamics

, Volume 20, Issue 1, pp 19–36 | Cite as

Kustaanheimo — Stiefel regularization and the quadrupolar conjugacy

  • Lei ZhaoEmail author


In this article, we first present the Kustaanheimo — Stiefel regularization of the spatial Kepler problem in a symplectic and quaternionic approach. We then establish a set of action-angle coordinates, the so-called LCF coordinates, of the Kustaanheimo — Stiefel regularized Kepler problem, which is consequently used to obtain a conjugacy relation between the integrable approximating “quadrupolar” system of the lunar spatial three-body problem and its regularized counterpart. This result justifies the study of Lidov and Ziglin [14] of the quadrupolar dynamics of the lunar spatial three-body problem near degenerate inner ellipses.


Kustaanheimo — Stiefel regularization quaternions symplectic reduction secular systems quadrupolar system 

MSC2010 numbers

70F07 70F16 37J15 


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Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Johann Bernoulli Institute for Mathematics and Computer ScienceUniversity of GroningenGroningenThe Netherlands

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