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A Four-Body Convex Central Configuration with Perpendicular Diagonals is Necessarily a Kite

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Abstract

We prove that any four-body convex central configuration with perpendicular diagonals must be a kite configuration. The result extends to general power-law potential functions, including the planar four-vortex problem.

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Acknowledgements

G. Roberts was supported by a grant from the National Science Foundation (DMS-1211675). M. Corbera and J. M. Cors were partially supported by MINECO grant MTM2013-40998-P; J. M. Cors was also supported by AGAUR grant 2014 SGR 568.

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Authors and Affiliations

  1. Departament de Tecnologies Digitals i de la Informació, Escola Politècnica Superior Universitat de Vic, C/Laura 13, 08500, Vic, Barcelona, Spain

    Montserrat Corbera

  2. Departament de Matemàtiques Escola Politècnica Superior d’Enginyeria de Manresa, Universitat Politècnica de Catalunya, Avda. de les Bases de Manresa 61-73, 08242, Manresa, Catalunya, Spain

    Josep M. Cors

  3. Department of Mathematics and Computer Science, College of the Holy Cross, 1 College Street, Worcester, MA, 01610, USA

    Gareth E. Roberts

Authors
  1. Montserrat Corbera
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  2. Josep M. Cors
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  3. Gareth E. Roberts
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Correspondence to Gareth E. Roberts.

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Corbera, M., Cors, J.M. & Roberts, G.E. A Four-Body Convex Central Configuration with Perpendicular Diagonals is Necessarily a Kite. Qual. Theory Dyn. Syst. 17, 367–374 (2018). https://doi.org/10.1007/s12346-017-0238-z

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  • DOI: https://doi.org/10.1007/s12346-017-0238-z

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Mathematics Subject Classfication

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