2014/10/09 by Lennard F. Bakker, Lennard Bakker, Bakker, Lennard +2
Mathematics · Physics and Astronomy · #Astro and Planetary Science #Classical mechanics #Computer science #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry #Hamiltonian (control theory) #Infinity #Invariant (physics) #Massless particle #Mathematical analysis #Mathematical physics #Mathematics #Motion (physics) #Newtonian fluid #Nuclear physics research studies #Phase space #Physics #Planar #Quantum chaos and dynamical systems #Quantum mechanics #Rigid body #Surface (topology) #Three-body problem #math.DS
paper · pdf · doi:10.48550/arxiv.1410.2636
published in arXiv (Cornell University) (Cornell University) · 24 pages, 15 figures
openalex publication_date 2014/10/09 · arxiv created 2014/11/11 · arxiv updated 2014/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the restricted n + 1-body problem of Newtonian mechanics. For periodic, planar configurations of n bodies which is symmetric under rotation by a fixed angle, the z-axis is invariant. We consider the effect of placing a massless particle on the z-axis. The study of the motion of this particle can then be modelled as a time-dependent Hamiltonian System. We give a geometric construction of a surface in the three-dimensional phase space separating orbits for which the massless particle escapes to infinity from those for which it does not. The construction is demonstrated numerically in a few examples