Symmetric Relative Equilibria in the Four-Vortex Problem with Three Equal Vorticities

Abstract

We examine in detail the relative equilibria of the 4-vortex problem when three vortices have equal strength, that is, ${\Gamma }_1={\Gamma }_2={\Gamma }_3=1$, and ${\Gamma }_4$ is a real parameter. We give the exact number of relative equilibria and bifurcation values. We also study the relative equilibria in the vortex rhombus problem.

21 pages, 4 figures. arXiv admin note: text overlap with arXiv:1301.6194 by other authors

References in corpus (1)

• Relative Equilibria in the Four-Vortex Problem with Two Pairs of Equal Vorticities

Cited by in corpus (2)

• On the Uniqueness of Co-circular Four Body Central Configurations
• Generic finiteness for a class of symmetric planar central configurations of the six-body problem and the six-vortex problem