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Solving Perturbed Kepler Problem by Quaternion Algebra
Department of Mathematics, Brock University, St. Catharines, Canada
- 1 Department of Mathematics, Brock University, St. Catharines, Canada
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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.
KeywordsQuaternionsKustaanheimo-Stiefel TransformationKepler ProblemPerturbation TheoryOrbital Elements
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