New formulation of the classical dynamics of the relativistic string with massive ends

Dynamic equations in the theory of a relativistic string with point masses at the ends are formulated only in terms of geometric invariants of the world trajectories of the massive ends of the string (curvature k1 and torsion k1 of the trajectories). These characteristics allow us to reproduce the string world surface up to shifts and rotations in the Minkowski space E21. The torsions k1(r) (1=1,2) obey a system of differential equations of the second order with shifted arguments describing the retardation effects of the interaction of masses through the string, k1 being constant. New particular solutions to these equations that correspond to periodic torsions will be discussed in the next paper. 12 refs