Geodesic
Action at a distance and equations of motion of a system of two massive points connected by a relativistic string
Teoretičeskaâ i matematičeskaâ fizika, Tome 89 (1991) no. 1, pp. 105-120 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $\mathbf E_2^1$ , these invariants – the curvature $k$ and torsion $\varkappa$ – 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 $k_i$, $i=1,2$, of the trajectories are constants that depend on the string tension and the masses at its ends, while the torsions $\varkappa_i(\tau)$, $i=1,2$, 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. 
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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. Teoretičeskaâ i matematičeskaâ fizika, Tome 89 (1991) no. 1, pp. 105-120. http://geodesic.mathdoc.fr/item/TMF_1991_89_1_a9/

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