A short study of a string on a plane: the energy and the effective mass

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.