2015/08/30 by Henk Broer, Lei Zhao, Broer, Henk +1
Physics and Astronomy · Engineering · #Astro and Planetary Science #Spacecraft Dynamics and Control #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1508.07589
In this article, we investigate the mathematical part of De Sitter's theory on the Galilean satellites, and further extend this theory by showing the existence of some quasi-periodic librating orbits by applications of KAM theorems. After showing the existence of De Sitter's family of linearly stable periodic orbits in the Jupiter-Io-Europa-Ganymede model by averaging and reduction techniques in the Hamiltonian framework, we further discuss the possible extension of this theory to include a fourth satellite Callisto, and establish the existence of a set of positive measure of quasi-periodic librating orbits in both models for almost all choices of masses.