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 TMF, 1991, Volume 89, Number 1, Pages 105–120 (Mi tmf5850)

Action at a distance and equations of motion of a system of two massive points connected by a relativistic string

B. M. Barbashov, A. M. Chervyakov

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 $\mathbf E_2^1$ , 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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English version:
Theoretical and Mathematical Physics, 1991, 89:1, 1087–1098

Bibliographic databases:

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

Citation in format AMSBIB
\Bibitem{BarChe91} \by B.~M.~Barbashov, A.~M.~Chervyakov \paper Action at a~distance and equations of motion of a~system of two massive points connected by a~relativistic string \jour TMF \yr 1991 \vol 89 \issue 1 \pages 105--120 \mathnet{http://mi.mathnet.ru/tmf5850} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1151374} \zmath{https://zbmath.org/?q=an:0780.53052|0733.53057} \transl \jour Theoret. and Math. Phys. \yr 1991 \vol 89 \issue 1 \pages 1087--1098 \crossref{https://doi.org/10.1007/BF01016809} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1991HT16100010} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. B. M. Barbashov, G. S. Sharov, “Initial-boundary problem for the relativistic string with massive ends”, Theoret. and Math. Phys., 101:2 (1994), 1332–1345
2. G. S. Sharov, “Determination of the world surface of a relativistic string from the trajectory of a massive end”, Theoret. and Math. Phys., 102:1 (1995), 109–115
3. G. S. Sharov, “Analogs of Fourier series for a relativistic string model with massive ends”, Theoret. and Math. Phys., 107:1 (1996), 487–498
4. V. P. Petrov, G. S. Sharov, “Classification of motions of a relativistic string with massive ends with linearizable boundary conditions”, Theoret. and Math. Phys., 109:2 (1996), 1388–1399
5. G. S. Sharov, “Solution of the initial boundary value problem for the relativistic string with massive ends”, Comput. Math. Math. Phys., 37:5 (1997), 590–601
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