Abstract
We study the cocircular relative equilibria (planar central configurations) in the four-vortex problem using methods suggested by the study of cocircular central configurations in the Newtonian four-body problem in recent work of Cors and Roberts. Using mutual distance coordinates, we show that the set of four-vortex relative equilibria is a two-dimensional surface with boundary curves representing kite configurations, isosceles trapezoids, and degenerate configurations with one zero vorticity. We also show that there is a constraint on the signs of the vorticities in these configurations; either three or four of the vorticities must have the same sign, in contrast to the noncocircular cases studied by Hampton, Roberts, and Santoprete.
Citation
Jonathan Gomez. Alexander Gutierrez. John Little. Roberto Pelayo. Jesse Robert. "Cocircular relative equilibria of four vortices." Involve 9 (3) 395 - 410, 2016. https://doi.org/10.2140/involve.2016.9.395
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