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Kustaanheimo, P., Schinzel, A., Davenport, H. and Stiefel, E. (1965) Perturbation Theory of Kepler Motion Based on Spinor Regularization. Journal für die reine und angewandte Mathematik, 1965, 204-219.
https://doi.org/10.1515/crll.1965.218.204

has been cited by the following article:

• TITLE: Solving Perturbed Kepler Problem by Quaternion Algebra

  AUTHORS: Jan Vrbik

  KEYWORDS: Quaternions, Kustaanheimo-Stiefel Transformation, Kepler Problem, Perturbation Theory, Orbital Elements

  JOURNAL NAME: Applied Mathematics, Vol.17 No.6, June 23, 2026

  ABSTRACT: In this article, we use quaternions together with Kustaanheimo-Stiefel transformation to solve the Kepler problem, first its unperturbed version and then when adding a small perturbing force. We assume that the perturbing force is autonomous, which enables us to derive a set of first-order differential equations for the corresponding orbital elements, while keeping them fully autonomous as well. This is achieved without compromising the resulting accuracy; there is no need for averaging out fast oscillations or involving a fast-angle variable. As a consequence, the equations can be solved to arbitrary accuracy by iterative and routine application of the new formulas.