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

Autor:	Abdalla Mansur, Muhammad Shoaib, Iharka Szücs-Csillik, Daniel Offin, Jack Brimberg, Hedia Fgaier
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	four-body problem action minimizing orbits celestial mechanics Mathematics QA1-939
Zdroj:	Mathematics, Vol 12, Iss 19, p 3152 (2024)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math12193152
Popis:	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.
Databáze:	Directory of Open Access Journals
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