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A Special Family of Stacked Central Configurations: Lagrange Plus Euler in One

  • J. Lino CornelioEmail author
  • M. Álvarez-Ramírez
  • Josep M. Cors
Article
  • 88 Downloads

Abstract

We show the existence of a family of stacked central configurations in the planar five-body problem with a special property. Three bodies \(m_1\), \(m_2\) and \(m_3\), ordered from left to right, are collinear and form an Euler central configuration, and the other two bodies \(m_4\) and \(m_5\), together with \(m_2\) are at the vertices of an equilateral triangle and form a Lagrange central configuration.

Keywords

Collinear central configurations Equilateral central configuration Laura-Andoyer equations 

Notes

Acknowledgements

The authors would like to thank the anonymous referee for valuable comments and suggestions, which help us to improve this paper.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • J. Lino Cornelio
    • 1
    Email author
  • M. Álvarez-Ramírez
    • 2
  • Josep M. Cors
    • 3
  1. 1.DACBUniversidad Juárez Autónoma de TabascoCunduacánMexico
  2. 2.Departamento de MatemáticasUAM–IztapalapaIztapalapa, México cityMexico
  3. 3.Departament de MatemàtiquesUniversitat Politècnica de CatalunyaManresaCatalonia

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