  We investigate the new special class of the finite string on a plane, after
the reduction from the relativistic $4D$ case. The suggested special form of
the phase space allows to define the extended Galilei group as a group of the
space - time symmetry for the considered system. The definition of the energy
for the studied non-relativistic string through the Cazimir function of this
group is suggested. The concept of the effective mass for the investigated
dynamical system is introduced. The appearance of strong correlations between
the degrees of freedom even on the classical level is discussed.
