The number of relative equilibria in the PCR4PB
Jordi-Llu\'is Figueras, Warwick Tucker, Piotr Zgliczynski
TL;DR
This paper introduces a new analytical method for accurately determining the number of relative equilibria in the planar, circular, restricted 4-body problem, enhancing computational efficiency and potentially aiding in solving more complex n-body problems.
Contribution
The paper presents a novel analytical approach that enables efficient computation of the exact number of relative equilibria in the PCR4PB, facilitating computer-aided proofs.
Findings
Efficient computation of relative equilibria counts.
Potential application to more complex n-body problems.
New analytical framework for celestial mechanics.
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.
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Taxonomy
TopicsSpacecraft Dynamics and Control · Stellar, planetary, and galactic studies · Astro and Planetary Science