2022/04/12 by Xijun Hu, Lei Liu, Hu, Xijun +5
Engineering · Physics and Astronomy · #Spacecraft Dynamics and Control #Astro and Planetary Science #Space Satellite Systems and Control
paper · pdf · doi:10.48550/arxiv.2204.05558
We study the spatial isosceles three body problem, which is a system with two degrees of freedom after modulo the rotation symmetry. For certain choices of energy and angular momentum, we find some disk-like global surfaces of section with the Euler orbit as their common boundary, and a brake orbit passing through them. By considering the Poincaré maps of these global surfaces of section, we prove the existence of all kinds of different periodic orbits under certain assumption. Moreover, we are able to prove, for generic choices of masses, the system always has infinitely many periodic orbits. One of the key is to estimate the rotation numbers of the Euler orbit and the brake orbit with respect to the Poincaré map. For this, we establish formulas connected these numbers with the mean indices of the corresponding orbits using the Maslov-type index.