ANALOGS OF FOURIER-SERIES FOR A RELATIVISTIC STRING MODEL WITH MASSIVE ENDS

A description of the motions of a relativistic string with massive end s (for the model with a finite mass on the first end and an infinite m ass on the second end) is proposed. This approach uses the expansion o f the string world surface into a series that is not reduced to the or dinary Fourier series due to the nonlinearity of the problem. The stat e equation of the string is derived from the mass shell condition for its end. The string motions are classified, allowing linearization of the boundary condition by a natural parametrization of the trajectory of the moving end. The set of such world surfaces is shown to be limit ed; for the special cases of 2 + 1- and 3 + 1-dimensional Minkowski sp aces, all of them reduce to a helicoid.