2014/06/17 by Gabriella Pinzari, Pinzari, Gabriella
Physics and Astronomy · Engineering · #Astro and Planetary Science #Spacecraft Dynamics and Control #Space Satellite Systems and Control
paper · pdf · doi:10.48550/arxiv.1406.4493
We improve a result in [L. Chierchia and G. Pinzari, Invent. Math. 2011] by proving the existence of a positive measure set of (3n-2)--dimensional quasi--periodic motions in the spacial, planetary (1+n)--body problem away from co--planar, circular motions. We also prove that such quasi--periodic motions reach with continuity corresponding (2n-1)--dimensional ones of the planar problem, once the mutual inclinations go to zero (this is related to a speculation in [V. I. Arnold. Russ. Math. Surv. 1963]). The main tool is a full reduction of the SO(3)--symmetry, which, in particular, retains symmetry by reflections and highlights a quasi--integrable structure, with a small remainder, independently of eccentricities and inclinations.