2011/12/08 by Francesco Paparella, Paparella, Francesco, Алессандро Порталури +2
Engineering · Mathematics · Physics and Astronomy · #70F10 (Primary) 37C80 (Secondary) #Aerospace Engineering and Energy Systems #Astro and Planetary Science #Dynamical Systems (math.DS) #FOS: Mathematics #Spacecraft Dynamics and Control #math.DS #msc:37C80 #msc:70F10
paper · pdf · doi:10.48550/arxiv.1112.1789
28 pages, 11 figures
arxiv created 2011/12/08 · openalex publication_date 2011/12/08 · arxiv updated 2011/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The goal of this paper is to give a detailed analytical description of the global dynamics of N points interacting through the singular logarithmic potential and subject to the following symmetry constraint: at each instant they form an orbit of the dihedral group of order 2l. The main device in order to achieve our results is a technique very popular in Celestial Mechanics, usually referred to as "McGehee transformation". After performing this change of coordinates that regularizes the total collision, we study the rest-points of the flow, the invariant manifolds and we derive interesting information about the global dynamics for l=2. We observe that our problem is equivalent to studying the geometry of stationary configurations of nearly-parallel vortex filaments in three dimensions in the LIA approximation.