The inverse problem for homothetic polygonal central configurations

  • Marcelo P. SantosEmail author
Original Article


We prove that, for some potentials (including the Newtonian one and the potential of Helmholtz vortices in the plane), central configurations with nonzero total mass consisting of two homothetic polygons of arbitrary size can only occur if the masses at each polygon are equal. The same result is true for many polygons as long as the ratios between the radii of the polygons are sufficiently large.


Celestial Mechanics N-Body problem N-Vortex problem Central configurations Relative equilibrium Polygonal central configuration 

Mathematics Subject Classification

70F10 70F15 70F17 70Fxx 37N05 



The author would like to thank Eduardo S. G. Leandro for being the advisor on this work and Thiago Dias for the helpful comments, as well as the Department of Mathematics at Universidade Federal Rural de Pernambuco for their assistance. We would like to thank the anonymous referees for their helpful comments and suggestions that improved an earlier version of this paper.

Compliance with ethical standards

Conflict of interest

The author declares that he has no conflict of interest.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Depto de MatemáticaUniversidade Federal Rural de PernambucoRecifeBrazil

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