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 E12 , these invariants – the curvature k and torsion ϰ – 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 ki, i=1,2, of the trajectories are constants that depend on the string tension and the masses at its
ends, while the torsions ϰi(τ), 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.
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
\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
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\mathscinet{http://mathscinet.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}
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Linking options:
https://www.mathnet.ru/eng/tmf5850
https://www.mathnet.ru/eng/tmf/v89/i1/p105
This publication is cited in the following 5 articles:
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
G. S. Sharov, “Analogs of Fourier series for a relativistic string model with massive ends”, Theoret. and Math. Phys., 107:1 (1996), 487–498
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
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
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