New Periodic Solutions for Three or Four Identical Vortices on a Plane and a Sphere
نویسندگان
چکیده
In this paper we describe new classes of periodic solutions for point vortices on a plane and a sphere. They correspond to similar solutions (so-called choreographies) in celestial mechanics. 1 Equations of motion and first integrals for vortices on a plane For n point vortices with Cartesian coordinates (xi, yi) and intensities Γi, the Hamiltonian equations of the motion are Γiẋi = ∂H ∂yi , Γiẏi = −∂H ∂xi , 1 6 i 6 n, (1) where the Hamiltonian is H = − 1 4π n
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