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
Voir la notice de l'article provenant de la source Math-Net.Ru
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.
@article{TMF_1991_89_1_a9,
author = {B. M. Barbashov and A. M. Chervyakov},
title = {Action at a~distance and equations of motion of a~system of two massive points connected by a~relativistic string},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {105--120},
publisher = {mathdoc},
volume = {89},
number = {1},
year = {1991},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1991_89_1_a9/}
}
TY - JOUR AU - B. M. Barbashov AU - A. M. Chervyakov TI - Action at a~distance and equations of motion of a~system of two massive points connected by a~relativistic string JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1991 SP - 105 EP - 120 VL - 89 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_1991_89_1_a9/ LA - ru ID - TMF_1991_89_1_a9 ER -
%0 Journal Article %A B. M. Barbashov %A A. M. Chervyakov %T Action at a~distance and equations of motion of a~system of two massive points connected by a~relativistic string %J Teoretičeskaâ i matematičeskaâ fizika %D 1991 %P 105-120 %V 89 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_1991_89_1_a9/ %G ru %F TMF_1991_89_1_a9
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/