INTEGRALS OF PERIODIC MOTION FOR CLASSICAL EQUATIONS OF RELATIVISTIC STRING WITH MASSES AT ENDS

Boundary equations for the relativistic string with masses at ends are formulated in terms of geometrical invariants of world trajectories o f masses at the string ends. In the three-dimensional Minkowski space E-2(1), there are two invariants of that sort, the curvature K and tor sion kappa. Curvatures of trajectories of the string massive ends are always constant, K-i = gamma/m(i)(i = 1,2,) whereas torsions kappa(i)( tau) are the functions of tau and obey a system of differential equati ons of second order with deviating arguments. For periodic torsions ka ppa(i)(tau + nl) = kappa(tau), where l is the string length in the pla ne of parameters tau and sigma(0 less than or equal to sigma less than or equal to l), these equations result in constant of motion.