On The Motion of Three Vortices

J. L. Synge

doi:10.4153/CJM-1949-022-2

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In a perfect incompressible fluid extending to infinity, the determination of the motion of N parallel rectilinear vortex filaments involves the solution of N non-linear differential equations, each of the first order. The method of Kirchhoff provides certain constants of the motion. If we describe the positions of the vortices by their point-traces on a plane perpendicular to them, the following facts follow from the theory of Kirchhoff:

(1.1) The mean centre of the system is fixed.

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