caa a22 4500 475805305 CHVBK 20180406123745.0 cr unu---uuuuu 170329e20000601xx s 000 0 eng 10.1007/s003329910015 doi (NATIONALLICENCE)springer-10.1007/s003329910015 Patrick G. W. Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, Saskatchewan, S7N 5E6, Canada, CA aut Dynamics of Perturbed Relative Equilibria of Point Vortices on the Sphere or Plane [Elektronische Daten] [G. W. Patrick] SO(3): , and there are stable relative equilibria of four point vortices, where three identical point vortices form an equilateral triangle circling a central vortex. These relative equilibria have zero (nongeneric) momentum and form a family that extends to arbitrarily small diameters. Using the energy-momentum method, I show their shape is stable while their location on the sphere is unstable, and they move, after perturbation to nonzero momentum, on the sphere as point particles move under the influence of a magnetic monopole. In the analysis the internal and external degrees of freedom are separated and the mass of these point particles determined. In addition, two identical such relative equilibria attract one another, while opposites repel, and in energetic collisions, opposites disintegrate to vortex pairs while identicals interact by exchanging a vortex. An analogous situation also occurs for the planar system with its noncompact SE(2) symmetry. Springer-Verlag New York Inc., 2000 Key words. Point vortex, collisions, relative equilibria, stability nationallicence Journal of Nonlinear Science Springer-Verlag 10/3(2000-06-01), 401-415 0938-8974 10:3<401 2000 10 332 https://doi.org/10.1007/s003329910015 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s003329910015 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Patrick G. W. Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, Saskatchewan, S7N 5E6, Canada, CA aut NATIONALLICENCE 773 0- Journal of Nonlinear Science Springer-Verlag 10/3(2000-06-01), 401-415 0938-8974 10:3<401 2000 10 332 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer