2017/10/07 by Gastón Beltritti, Beltritti, Gastón, Fernando Mazzone +3
Engineering · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Spacecraft Dynamics and Control #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1710.02667
arxiv created 2017/10/07 · openalex publication_date 2017/10/07 · arxiv updated 2017/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we address a n+1-body gravitational problem governed by the Newton's laws, where n primary bodies orbit on a plane Π and an additional massless particle moves on the perpendicular line to Π passing through the center of mass of the primary bodies. We find a condition for that the configuration described be possible. In the case that the primaries are in a rigid motion we classify all the motions of the massless particle. We study the situation when the massless particle has a periodic motion with the same minimal period than primary bodies. We show that this fact is related with the existence of certain pyramidal central configuration.