Integrals of periodic motion for classical equations of relativistic string with masses at ends

Abstract

Boundary equations for the relativistic string with masses at ends are formulated in terms of geometrical invariants of world trajectories of masses at the string ends. In the three-dimensional Minkowski space , there are two invariants of that sort, the curvature K and torsion . Curvatures of trajectories of the string massive ends are always constant, , whereas torsions are the functions of and obey a system of differential equations of second order with deviating arguments. For periodic torsions , where l is the string length in the plane of parameters and , these equations result in constant of motion.