Quaternions and the perturbed Kepler problem

Abstract

Quaternions, introduced by Hamilton (Philos. Mag. 25, 489-495, 1844) as a generalization of complex numbers, lead to a remarkably simple representation of the perturbed three-dimensional Kepler problem as a perturbed harmonic oscillator. The paper gives an overview of this technique, including an outlook to applications in perturbation theories. © Springer Science+Business Media B.V. 2006.