Geodesic
Thomson's configurations in dynamics of two vortices in an annular region
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2010), pp. 71-76 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

For the system of two point vortices in anulus the Hamiltonian is expressed in terms of elliptic functions. The stability of the Thomson configuration is studied.
Mots-clés : point vortex, Thomson configuration
Keywords: elliptic functions, stability. 
@article{VUU_2010_4_a7,
     author = {N. N. Erdakova},
     title = {Thomson's configurations in dynamics of two vortices in an annular region},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {71--76},
     year = {2010},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2010_4_a7/}
}
TY  - JOUR
AU  - N. N. Erdakova
TI  - Thomson's configurations in dynamics of two vortices in an annular region
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2010
SP  - 71
EP  - 76
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VUU_2010_4_a7/
LA  - ru
ID  - VUU_2010_4_a7
ER  - 
%0 Journal Article
%A N. N. Erdakova
%T Thomson's configurations in dynamics of two vortices in an annular region
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2010
%P 71-76
%N 4
%U http://geodesic.mathdoc.fr/item/VUU_2010_4_a7/
%G ru
%F VUU_2010_4_a7
N. N. Erdakova. Thomson's configurations in dynamics of two vortices in an annular region. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2010), pp. 71-76. http://geodesic.mathdoc.fr/item/VUU_2010_4_a7/

[1] Agostinelli C., “Applicazione del metido delle immagini alla determinazione del moto liquido piano in una corona circolare in cui si formino dei vortici puntiformi. Problemi elettrostatici correspondenti”, Rend. Ist. Lomb. Sci. Lett. (3), 6 (1942), 669–689 | MR | Zbl

[2] Borisov A. V., Mamaev I. S., Kilin A. A., “Absolute and relative choreographies in the problem of point vortices moving on a plane”, Regul. Chaotic Dyn., 9:2 (2004), 101–112 | DOI | MR

[3] Fetter A., “Low-lying superfluid states in a rotating annulus”, Phys. Rev., 153:1 (1967), 285–296 | DOI | Zbl

[4] Lakaniemi M., On the dynamics of point vortices in a quantum gas confined in an annular region, arXiv: 0708.1898v3

[5] Abramovits M., Stigan I., Spravochnik po spetsialnym funktsiyam, Nauka, M., 1979 | MR

[6] Borisov A. V., Bolsinov A. V., Mamaev I. S., “Topologiya i ustoichivost integriruemykh sistem”, UMN, 65:2(392) (2010), 71–132 | DOI | MR | Zbl

[7] Borisov A. V., Mamaev I. S., Matematicheskie metody dinamiki vikhrevykh struktur, Inst. kompyutern. issl., M.–Izhevsk, 2005 | MR

[8] Zueva T. I., “Dvizhenie vikhrei v koltsevoi oblasti”, Fizika nizkikh temperatur, 26:2 (2000), 119–127 | MR

[9] Vaskin V. V., Erdakova N. N., “Dinamika dvukh tochechnykh vikhrei v koltsevoi oblasti”, Nelineinaya dinamika, 6:3 (2010), 531–547

[10] Havelock T. H., “The stability of motion of rectilinear vortices in ring formation”, Philos. Mag. (7), 11 (1931), 617–633 | Zbl