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

TL;DR

This paper derives boundary equations for a relativistic string with masses at its ends using geometric invariants, and finds constants of motion for periodic torsion in three-dimensional Minkowski space.

Contribution

It formulates boundary equations in terms of geometric invariants and identifies constants of motion for periodic torsion, advancing understanding of relativistic string dynamics.

Findings

Boundary equations expressed via curvature and torsion.

Constants of motion identified for periodic torsion.

Analysis conducted in 3D Minkowski space.

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 $E^1_2$, there are two invariants of that sort, the curvature $K$ and torsion $\kappa$. For these equations of motion with periodic $\kappa_i(\tau+n l)=\kappa(\tau)$, constants of motion are obtained.