Abstract:
Dynamical equations in the theory of a relativistic string with point masses at the ends are formulated solely in terms of geometrical invariants of the worldlines of the massive ends of the string. In three-dimensional Minkowski space E12 , these invariants – the curvature k and torsion ϰ – make it possible to completely recover the world surface of the string up to its position as a whole. It is shown that the curvatures ki, i=1,2, of the trajectories are constants that depend on the string tension and the masses at its
ends, while the torsions ϰi(τ), i=1,2, satisfy a system of second-order differential equations with shifted arguments. A new exact solution
of these equations in the class of elliptic functions is obtained.
Citation:
B. M. Barbashov, A. M. Chervyakov, “Action at a distance and equations of motion of a system of two massive points connected by a relativistic string”, TMF, 89:1 (1991), 105–120; Theoret. and Math. Phys., 89:1 (1991), 1087–1098