Periodic Solutions with Singularities in Two Dimensions in the n-body Problem

2008/11/03 by Tiancheng Ouyang, Ouyang, Tiancheng, Skyler Simmons +3
Engineering · Physics and Astronomy · #70F10 #Astro and Planetary Science #Dynamical Systems (math.DS) #FOS: Mathematics #Space Satellite Systems and Control #Spacecraft Dynamics and Control

paper · pdf · doi:10.48550/arxiv.0811.0227

openalex publication_date 2008/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Analytical methods are used to prove the existence of a periodic, symmetric solution with singularities in the planar 4-body problem. A numerical calculation and simulation are used to generate the orbit. The analytical method easily extends to any even number of bodies. Multiple simultaneous binary collisions are a key feature of the orbits generated.

Citations

• Linear Stability of the Elliptic Lagrangian Triangle Solutions in the Three-Body Problem

Related

• Periodic Solutions with Alternating Singularities in the Collinear Four-body Problem
• Symmetric Periodic Orbits in Three Sub-Problems of the N-body Problem
• Symmetric orbits arising from Figure-Eight for N-body problem
• Really perverse periodic solutions of the planar N-body problem
• New Periodic Orbits for the n-Body Problem