Qualitative Theory of Dynamical Systems

, Volume 8, Issue 2, pp 349-356

First online:

Finiteness of Kite Relative Equilibria in the Five-Vortex and Five-Body Problems

  • Marshall HamptonAffiliated withDepartment of Mathematics and Statistics, University of Minnesota Email author 

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We study the finiteness of planar relative equilibria of the Newtonian five-body problem and in the five-vortex problem in the case that configurations form a symmetric kite (three points on a line and two additional points placed symmetrically with respect to that line). We can prove that the equivalence classes of such relative equilibria are finite with some possible exceptional cases. These exceptional cases are given explicitly as polynomials in the masses (or vorticities in the vortex problem). These results depend on computations performed with the software Sage, Singular, Magma, and Gfan.


Celestial mechanics n-Body problem Relative equilibria Vortices Tropical geometry

Mathematics Subject Classification (2000)

70F10 70F15 37N05 76B47