Quaternions and the perturbed Kepler problem [chapter]

Jörg Waldvogel
Periodic, Quasi-Periodic and Chaotic Motions in Celestial Mechanics: Theory and Applications  
Quaternions, introduced by W. R. Hamilton (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.
doi:10.1007/978-1-4020-5325-2_11 fatcat:64f5ch4tlva7hkezlrkc42c7m4