Vol. 9, No. 3, 2016

Download this article
Download this article For screen
For printing
Recent Issues

Volume 11, 1 issue

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
Cover Page
Editorial Board
Editors’ Addresses
Editors’ Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Ethics Statement
Subscriptions
Editorial Login
Author Index
Coming Soon
Contacts
 
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Cocircular relative equilibria of four vortices

Jonathan Gomez, Alexander Gutierrez, John Little, Roberto Pelayo and Jesse Robert

Vol. 9 (2016), No. 3, 395–410
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.

Keywords
relative equilibria, vortices, central configurations
Mathematical Subject Classification 2010
Primary: 76B99
Secondary: 70F10, 13P10
Milestones
Received: 14 November 2014
Revised: 12 March 2015
Accepted: 9 May 2015
Published: 3 June 2016

Communicated by Martin Bohner
Authors
Jonathan Gomez
Department of Mathematics
University of Hawai’i at Manoa
Honolulu, HI 96822
United States
Alexander Gutierrez
Department of Mathematics
University of Minnesota
Minneapolis, MN 55455
United States
John Little
Department of Mathematics and Computer Science
College of the Holy Cross
Worcester, MA 01610
United States
Roberto Pelayo
Department of Mathematics
University of Hawai’i at Hilo
Hilo, HI 96720
United States
Jesse Robert
Department of Mathematics
University of Hawai’i at Hilo
Hilo, HI 96720
United States