Geodesic
A new integrable problem of motion of point vortices on the sphere
Russian journal of nonlinear dynamics, Tome 3 (2007) no. 2, pp. 211-223 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The dynamics of an antipodal vortex on a sphere (a point vortex plus its antipode with opposite circulation) is considered. It is shown that the system of $n$ antipodal vortices can be reduced by four dimensions (two degrees of freedom). The cases $n=2,3$ are explored in greater detail both analytically and numerically. We discuss Thomson, collinear and isosceles configurations of antipodal vortices and study their bifurcations.
Keywords: hydrodynamics, ideal fluid, vortex dynamics, reduction, bifurcation analysis.
Mots-clés : point vortex 
@article{ND_2007_3_2_a5,
     author = {A. V. Borisov and A. A. Kilin and I. S. Mamaev},
     title = {A new integrable problem of motion of point vortices on the sphere},
     journal = {Russian journal of nonlinear dynamics},
     pages = {211--223},
     year = {2007},
     volume = {3},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2007_3_2_a5/}
}
TY  - JOUR
AU  - A. V. Borisov
AU  - A. A. Kilin
AU  - I. S. Mamaev
TI  - A new integrable problem of motion of point vortices on the sphere
JO  - Russian journal of nonlinear dynamics
PY  - 2007
SP  - 211
EP  - 223
VL  - 3
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/ND_2007_3_2_a5/
LA  - ru
ID  - ND_2007_3_2_a5
ER  - 
%0 Journal Article
%A A. V. Borisov
%A A. A. Kilin
%A I. S. Mamaev
%T A new integrable problem of motion of point vortices on the sphere
%J Russian journal of nonlinear dynamics
%D 2007
%P 211-223
%V 3
%N 2
%U http://geodesic.mathdoc.fr/item/ND_2007_3_2_a5/
%G ru
%F ND_2007_3_2_a5
A. V. Borisov; A. A. Kilin; I. S. Mamaev. A new integrable problem of motion of point vortices on the sphere. Russian journal of nonlinear dynamics, Tome 3 (2007) no. 2, pp. 211-223. http://geodesic.mathdoc.fr/item/ND_2007_3_2_a5/