Abstract
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.
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Zhao, L. Kustaanheimo — Stiefel regularization and the quadrupolar conjugacy. Regul. Chaot. Dyn. 20, 19–36 (2015). https://doi.org/10.1134/S1560354715010025
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DOI: https://doi.org/10.1134/S1560354715010025