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Stacked Central Configurations in the 5-Vortex Problem

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Abstract

In this paper, we study two classes of symmetric central configurations in the 5-vortex problem, namely the case with three vortices located at the vertices of an equilateral triangle and two vortices located symmetrically with respect to a perpendicular bisector of the triangle and the case with three vortices located at the vertices of an equilateral triangle and two vortices located at one mediatrix of the triangle. We classify all the possible arrangements for the circulations in such central configurations with analytic proofs. Also, we analyze the possibility of a central configuration such that it is stacked in two ways, Euler plus two or Lagrange plus two, simultaneously, more specifically one subset with three collinear positions in central configuration and another subset with three positions in the equilateral triangle in central configuration.

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The data that support the findings of this study are available from the corresponding author upon reasonable request

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Acknowledgements

The first author is partially supported Convenio Marco UBB1755/2016-2020 No. 84, FAPEMIG APQ-03149-18 and CNPq 433285/2018-4 . The second author is partially supported by Math Amsud-Conicyt 17-Math-07 and Fondecyt 1180288.

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Authors and Affiliations

  1. Instituto de Matemática e Computação, Universidade Federal de Itajubá, Itajubá, MG, Brazil

    A. C. Fernandes

  2. Grupo de Investigación en Sistemas Dinámicos y Aplicaciones-GISDA, Departamento de Matemática, Universidad del Bío-Bío, Concepción, Chile

    Claudio Vidal

Authors
  1. A. C. Fernandes
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  2. Claudio Vidal
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Correspondence to A. C. Fernandes.

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Communicated by Eva Kanso.

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Fernandes, A.C., Vidal, C. Stacked Central Configurations in the 5-Vortex Problem. J Nonlinear Sci 31, 83 (2021). https://doi.org/10.1007/s00332-021-09741-1

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