  The Letter considers dynamics of helical vortices and helical-vortex rings
either solving directly the equations of motions of a vortex line or using
canonical relations following from the Hamiltonian equations of motion. An
analytical solution in elliptical integrals was found for helical-vortex rings
in the local-induction approximation. The analysis based on the canonical
Hamilton relation provides a clear physical explanation for anomalous
velocities of helical-vortex rings, i.e., for suppression of the velocity and
even inversion of its direction at sufficiently large amplitude of the helical
distortion. The extended local-induction approximation is suggested, which
provides an exact solution for the equations of motion of helical vortices and
helical-vortex rings in the limit when the small-pitch helical vortex reduces
to a cylindric sheet of uniform vorticity.
