On equilateral central configurations in the 1+4-body problem
Álvarez Ramírez, Martha (Universidad Autónoma Metropolitana - Iztapalapa. Departamento de Matemáticas)
Barrabés Vera, Esther (Universitat de Girona. Departament d'Informàtica, Matemàtica Aplicada i Estadística)
Cors Iglesias, Josep Maria (Universitat Politècnica de Catalunya. Departament de Matemàtiques)

Date:	2026
Abstract:	We investigate central configurations in the planar five-body problem with one dominant mass. The remaining four masses, referred to as coorbital satellites, are infinitesimal and positioned along a circle centered at the big mass. We focus on stacked relative equilibria in which the central body and two fixed satellites form an equilateral triangle, while the two remaining satellites occupy distinct positions on the unit circle. In the limiting case when the small masses tend to zero, the problem naturally divides into three scenarios depending on the location of these remaining bodies relative to the arc formed by the two fixed satellites. We show that the first case, in which both satellites lie inside the arc, cannot occur under the positivity constraint on the masses. The second case, where one satellite lies inside the arc and the other outside, admits solutions that we characterize in detail, while the third case, with both satellites outside the arc, leads to a richer family of admissible configurations.
Grants:	Agencia Estatal de Investigación PID2021-123968NB-I00 Agencia Estatal de Investigación PID2022-136613NB-I00
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	5-body problem ; Convex central configuration ; Equilateral triangle ; Coorbital
Published in:	Communications in nonlinear science and numerical simulation, Vol. 152, Num. PartD (January 2026) , art. 109365, ISSN 1878-7274

DOI: 10.1016/j.cnsns.2025.109365

14 p, 3.2 MB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles