The number of relative equilibria in the PCR4PB

2022/04/19 by Jordi-Lluís Figueras, Figueras, Jordi-Lluís, Warwick Tucker +3 · 1 citation
Engineering · Physics and Astronomy · #Spacecraft Dynamics and Control #Stellar, planetary, and galactic studies #Astro and Planetary Science

paper · pdf · doi:10.48550/arxiv.2204.08812

Abstract

The aim of this paper is to present a new, analytical, method for computing the exact number of relative equilibria in the planar, circular, restricted 4-body problem of celestial mechanics. The new approach allows for a very efficient computer-aided proof, and opens a potential pathway to proving harder instances of the n-body problem.

Cited by

• Degeneracy of Planar Central Configurations in the N-Body Problem

Related

• Finiteness of classes of relative equilibria for the n-body problem
• On the minimum distance between masses of relative equilibria of the n-body problem
• On the n-body problem in ℝ⁴
• Linear stability of the elliptic relative equilibria for the restricted 4-body problem: the Euler case
• Really perverse periodic solutions of the planar N-body problem