Analogs of Fourier series for a relativistic string model with massive ends

A description of motions of a relativistic string with massive ends (for the model with a finite mass on the first end and infinite one on the second end) is proposed. This approach uses the expansion of the string world surface in a series that doesn't reduce to the usual Fourier series due to nonlinearity of the problem. A state equation of the string resultes from the mass shell condition of its end. World surfaces of this string, on which linearization of a boundary condition due to natural parametrization of moving end trajectory is possible, are classified. The set of such world surfaces is shown to be limited in particular in 2+1- and 3+1-dimensional Minkowski spaces all of them reduce to the helicoid.