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 
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/
@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},
     year = {1991},
     volume = {89},
     number = {1},
     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
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
%U http://geodesic.mathdoc.fr/item/TMF_1991_89_1_a9/
%G ru
%F TMF_1991_89_1_a9

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.

[1] Barbashov B. M., Nesterenko V. V., Introduction to the relativistic string theory, World Scientific, Singapore, 1990 | MR | Zbl

[2] Wheeler J. A., Feynman R. P., Rev. Mod. Phys., 17 (1945), 157–168 | DOI

[3] Chernikov N. A., Shavokhina N. S., TMF, 42:1 (1980), 59–70 ; 43:3, 356–366 ; Шавохина Н. С., ДАН СССР, 265 (1982), 852–856 | MR | Zbl | MR | Zbl | MR

[4] Eisenhart L. P., A treatise on the differential geometry of curves and surfaces, Dover, New York, 1960 | MR

[5] Barbashov B. M., Chervyakov A. M., TMF, 74:3 (1988), 430–439 | MR | Zbl

[6] Chodos A., Thorn C. B., Nucl. Phys., B72 (1974), 509–522 | DOI

[7] Frampton P. H., Phys. Rev., D12 (1975), 538–545

[8] Nesterenko V. V., TMF, 71:2 (1987), 238–248

[9] Barbashov B. M., Nucl. Phys., B129 (1977), 175–188 | DOI

[10] Gervais J. L., Neveu A., Nucl. Phys., B199 (1982), 59–76 ; Johansson L., Kihlberg A., Marnelius R., Sectors of solutions and minimal energies in classical Liouville theories for strings, Report ITP 83-8, ITP, Goteborg, 1983 | DOI | MR | MR

[11] Gursa E., Kurs matematicheskogo analiza. T. 2. Ch. 1. Teoriya analiticheskikh funktsii, GTTI, M., 1933

[12] Nesterenko V. V., Z. Phys., 47 (1990), 111–114