2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/187226Boundary 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 $E^1_2$, there are two invariants of that sort, the curvature $K$ and torsion $κ$. Curvatures of trajectories of the string ends with masses are always constant, $K_i = γ/m_i (i =1,2,)$, whereas torsions $κ_i(τ)$ obey a system of differential equations with deviating arguments. For these equations with periodic $κ_i(τ+n l)=κ(τ)$, constants of motion are obtained (part I) and exact solutions are presented (part II) for periods $l$ and $2l$ where $l$ is the string length in the plane of parameters $τ$ and $σ\ (σ_1 = 0, σ_2 =l)$.15 pagesHigh Energy Physics - Theorytext