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Cocircular
relative equilibria of four vortices
Jonathan Gomez, Alexander Gutierrez, John Little, Roberto Pelayo and Jesse Robert
Vol. 9 (2016), No. 3, 395–410
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Abstract |
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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. |
Keywords
relative equilibria, vortices, central configurations
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Mathematical Subject Classification 2010
Primary: 76B99
Secondary: 70F10, 13P10
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Milestones
Received: 14 November 2014
Revised: 12 March 2015
Accepted: 9 May 2015
Published: 3 June 2016
Communicated by Martin Bohner
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Authors |
| Jonathan Gomez | |
| Department of Mathematics University of Hawai’i at Manoa Honolulu, HI 96822 United States |
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| Alexander Gutierrez | |
| Department of Mathematics University of Minnesota Minneapolis, MN 55455 United States |
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| John Little | |
| Department of Mathematics and
Computer Science College of the Holy Cross Worcester, MA 01610 United States |
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| Roberto Pelayo | |
| Department of Mathematics University of Hawai’i at Hilo Hilo, HI 96720 United States |
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| Jesse Robert | |
| Department of Mathematics University of Hawai’i at Hilo Hilo, HI 96720 United States |
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