On the motion of two-dimensional vortices with mass
The Helmholtz-Kirchhoff ODEs governing the planar motion of \(N\) point vortices in an ideal, incompressible fluid are extended to the case where the fluid has impurities. In this case the resulting ODEs have an additional inertia-type term, so the point vortices are termed massive. Using the symmetries, we reduce the four degrees of freedom system of two ``massive'' vortices to two degrees of freedom system. We exhibit an integrable case and a nonintegrable one, according to choices of parameters. Finally, we discuss the behavior of solutions as the masses of the vortices tend to zero, using for initial conditions a point of the trajectory of the Helmholtz-Kirchhoff equations.
scientific article; zbMATH DE number 679531
scientific article