@article{Mansur2023, 
author = {Abdalla Mansur and Muhammad Shoaib and Iharka Szücs-Csillik and Daniel Offin and Jack Brimberg},
title = {Action minimizing orbits in the trapezoidal four body problem},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {8},
pages = {17650-17665},
keywords = {minimizers, central configuration, four-body problem, trapezoidal problem, action functional, homographic solutions},
url = {https://www.sciopen.com/article/10.3934/math.2023901},
doi = {10.3934/math.2023901},
abstract = {In this paper, we study the minimizing property for the isosceles trapezoid solutions of the four-body problem. We prove that the minimizers of the action functional restricted to homographic solutions are the Keplerian elliptical solutions, and this functional has a minimum equal to        3    2    (  2  π      )          2              /            3            T          1              /            3                  (                        ξ          (          a          ,          b          )                          η          (          a          ,          b          )                    )              2              /            3      . Further, we investigate the dynamical behavior in the trapezoidal four-body problem using the Poincaré surface of section method.}
}