Geodesic
Dynamics of two vortices on a finite flat cylinder
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 33 (2023) no. 4, pp. 642-658

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In this work, a model that describes the motion of point vortices in an ideal incompressible fluid on a finite flat cylinder is obtained. The case of two vortices is considered in detail. It is shown that the equations of motion of vortices can be represented in Hamiltonian form and have an additional first integral. A procedure of reduction to a fixed level of the first integral is proposed. For the reduced system, phase portraits are constructed, fixed points and singularities of the system are indicated.
Keywords: point vortices, ideal fluid, fixed points, singularities
Mots-clés : phase portrait 
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     author = {E. M. Artemova},
     title = {Dynamics of two vortices on a finite flat cylinder},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {642--658},
     publisher = {mathdoc},
     volume = {33},
     number = {4},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2023_33_4_a6/}
}
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E. M. Artemova. Dynamics of two vortices on a finite flat cylinder. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 33 (2023) no. 4, pp. 642-658. http://geodesic.mathdoc.fr/item/VUU_2023_33_4_a6/