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 TMF, 1988, Volume 74, Number 3, Pages 430–439 (Mi tmf4507)

Geometrical method of solving the boundary-value problem in the theory of a relativistic string with masses at its ends

B. M. Barbashov, A. M. Chervyakov

Abstract: A differential-geometric formulation of the dynamics of a relativistic string with masses at its ends is considered in the Minkowski space $E_2^1$. The surface swept out by the string is described by differential forms and is bounded by two curves – the worldlines of its massive ends. These curves have a constant geodesic curvature, and their torsion is determined only up to an arbitrary function on the interval $[0,2\pi]$. Equations are obtained that determine the world surface of the string as a function of the curvature and torsion of the trajectories of its massive ends. For the choice of the constant torsions for which the mass points move along helices, the surface of the relativistic string is a helicoid.

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English version:
Theoretical and Mathematical Physics, 1988, 74:3, 292–299

Bibliographic databases:

Citation: B. M. Barbashov, A. M. Chervyakov, “Geometrical method of solving the boundary-value problem in the theory of a relativistic string with masses at its ends”, TMF, 74:3 (1988), 430–439; Theoret. and Math. Phys., 74:3 (1988), 292–299

Citation in format AMSBIB
\Bibitem{BarChe88} \by B.~M.~Barbashov, A.~M.~Chervyakov \paper Geometrical method of solving the boundary-value problem in the theory of a~relativistic string with masses at its ends \jour TMF \yr 1988 \vol 74 \issue 3 \pages 430--439 \mathnet{http://mi.mathnet.ru/tmf4507} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=953301} \zmath{https://zbmath.org/?q=an:0661.53004} \transl \jour Theoret. and Math. Phys. \yr 1988 \vol 74 \issue 3 \pages 292--299 \crossref{https://doi.org/10.1007/BF01016623} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1988U172700010} 

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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, A. M. Chervyakov, “Action at a distance and equations of motion of a system of two massive points connected by a relativistic string”, Theoret. and Math. Phys., 89:1 (1991), 1087–1098
2. 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
3. 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
4. G. S. Sharov, “Analogs of Fourier series for a relativistic string model with massive ends”, Theoret. and Math. Phys., 107:1 (1996), 487–498
5. 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
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