Periodic and Quasi-Periodic Orbits in the Collinear Four-Body Problem: A Variational Analysis

Abdalla Mansur (), Muhammad Shoaib, Iharka Szücs-Csillik (), Daniel Offin, Jack Brimberg and Hedia Fgaier
Additional contact information
Abdalla Mansur: Libyan Center for Engineering Research and Information Technology, Bani Waleed 637211, Libya
Muhammad Shoaib: Smart and Scientific Solutions, 32 Allerdyce Drive, Glasgow G15 6RY, Scotland, UK
Iharka Szücs-Csillik: Romanian Academy, Astronomical Institute, Astronomical Observatory Cluj-Napoca, 400487 Cluj-Napoca, Romania
Daniel Offin: Department of Mathematics and Statistics, Queen’s University, Kingston, ON K7L 3N6, Canada
Jack Brimberg: Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, ON K7K 7B4, Canada
Hedia Fgaier: Department of Mathematics, Full Sail University, Winter Park, FL 32792, USA

Mathematics, 2024, vol. 12, issue 19, 1-17

Abstract: This paper investigated the periodic and quasi-periodic orbits in the symmetric collinear four-body problem through a variational approach. We analyze the conditions under which homographic solutions minimize the action functional. We compute the minimal value of the action functional for these solutions and show that, for four equal masses organized in a linear configuration, these solutions are the minimizers of the action functional. Additionally, we employ numerical experiments using Poincaré sections to explore the existence and stability of periodic and quasi-periodic solutions within this dynamical system. Our results provide a deeper understanding of the variational principles in celestial mechanics and reveal complex dynamical behaviors, crucial for further studies in multi-body problems.

Keywords: four-body problem; action minimizing orbits; celestial mechanics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/19/3152/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/19/3152/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:19:p:3152-:d:1494550

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().