On the mechanics of helical flows in an ideal incompressible viscous continuous medium

We find a general solution to the problem on the motion in an incompressible continuous medium occupying at any time a whole domain $D\subset R^3$ under the conditions that $D$ is an axially symmetric cylinder and the motion is described by the Euler equation together with the continuity equation for an incompressible medium and belongs to the class of planar-helical flows (according to I. S. Gromeka's terminology), in which sreamlines coincide with vortex lines. This class is constructed by the method of transformation of the geometric structure of a vector field. The solution is characterized in Theorem 2 in the end of the paper.