Exact solutions in the theory of a relativistic string with mass at ends

Exact solution in the theory of a relativistic string with masses at ends forthree-dimensional space-time is constructed. The solution includes one scalar function of one variable complying with a simple periodicity condition which permits to represent it as the Fourrier series. This solution describes such motion of the relativistic string when projections of world trajectories of its massive ends on spatial plane are circumfe-- rences. In addition to orthogonal gauge supplementary gauge conditions are imposed and polar splace coordinates are used. It is shown how the relativistic string with massive ends rotating as the whole in the given plane is described in this approach