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

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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.

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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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Authors and Affiliations

  1. DACB, Universidad Juárez Autónoma de Tabasco, 86690, Cunduacán, Tabasco, Mexico

    J. Lino Cornelio

  2. Departamento de Matemáticas, UAM–Iztapalapa, 09340, Iztapalapa, México city, Mexico

    M. Álvarez-Ramírez

  3. Departament de Matemàtiques, Universitat Politècnica de Catalunya, 08242, Manresa, Catalonia

    Josep M. Cors

Authors
  1. J. Lino Cornelio
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  2. M. Álvarez-Ramírez
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  3. Josep M. Cors
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Corresponding author

Correspondence to J. Lino Cornelio.

Additional information

J. Lino Cornelio is supported by a CONACyT graduate grant. M. Alvarez-Ramírez was partially supported by the grant: Red de cuerpos académicos Ecuaciones Diferenciales. Proyecto sistemas dinámicos y estabilización. PRODEP 2011-SEP, Mexico. J. M. Cors was partially supported by MINECO Grant MTM2013-40998-P, MTM2016-77278-P (FEDER) and AGAUR Grant 2014 SGR 568.

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Cornelio, J.L., Álvarez-Ramírez, M. & Cors, J.M. A Special Family of Stacked Central Configurations: Lagrange Plus Euler in One. J Dyn Diff Equat 31, 711–718 (2019). https://doi.org/10.1007/s10884-018-9647-1

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  • DOI: https://doi.org/10.1007/s10884-018-9647-1

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