About the non-standard viewpoint on the dynamics of closed vortex filament

Abstract

In this article we construct the Hamiltonian description of the closed vortex filament dynamics in terms of non-standard variables, phase space and constraints. The suggested approach makes obvious interpretation of considered system as a quasiparticle that possess certain external and internal degrees of the freedom. The constructed theory is invariant under the transformation of Galilei group. The appearance of this group allows for a new viewpoint on the energy of a closed vortex filament with zero thickness. The explicit formula for the effective mass of the quasiparticle 'closed vortex filament' is suggested.