We use Jacobi coordinates and a momentum map/Lie-Poisson reduction to derive a system of equations for the three-vortex problem with no coordinate singularities and use it to …
We use Jacobi coordinates and Nambu brackets to derive a new representation of the motion of three vortices which, unlike all previous reductions, introduces no singularities into …
A complete English translation of Walter Gröbli's 1877 Ph.D. Thesis, together with some notes on the process. The work considers the dynamics of point vortices in a two-dimensional …
We show via analytical perturbation theory that the leapfrogging vortex quartet becomes unstable exactly at the critical ratio $\alpha= \phi^{-2}.$
We investigate the stability of a one-parameter family of periodic solutions of the four-vortex problem known as _leapfrogging_ orbits. These solutions, which consists of two pairs …
We study the motion of a vortex dipole in a Bose-Einstein condensate confined to an anisotropic trap. We focus on a system of ordinary differential equations describing the …