Trapezoid central configurations

Montserrat Corbera, Josep M. Cors, Jaume Llibre, Ernesto Pérez-Chavela

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5 Citations (Scopus)

Abstract

© 2018 Elsevier Inc. We classify all planar four–body central configurations where two pairs of the bodies are on parallel lines. Using cartesian coordinates, we show that the set of four–body trapezoid central configurations with positive masses forms a two–dimensional surface where two symmetric families, the rhombus and isosceles trapezoid, are on its boundary. We also prove that, for a given position of the bodies, in some cases a specific order of the masses determines the geometry of the configuration, namely acute or obtuse trapezoid central configuration. We also prove the existence of non–symmetric trapezoid central configurations with two pairs of equal masses.
Original languageEnglish
Pages (from-to)127-142
JournalApplied Mathematics and Computation
Volume346
DOIs
Publication statusPublished - 1 Apr 2019

Keywords

  • 4-body problem
  • Convex central configurations
  • Trapezoidal central configurartions

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    Corbera, M., Cors, J. M., Llibre, J., & Pérez-Chavela, E. (2019). Trapezoid central configurations. Applied Mathematics and Computation, 346, 127-142. https://doi.org/10.1016/j.amc.2018.10.066