Geodesic
Classification of motions of a~relativistic string with massive ends with linearizable boundary conditions
Teoretičeskaâ i matematičeskaâ fizika, Tome 109 (1996) no. 2, pp. 187-201

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We classified all motions (world surfaces) of a relativistic string with massive ends, for which equations of motion and boundary conditions can be linearized through a natural parametrization of the end's trajectories. These motions can be represented as Fourier series with eigenfunctions of some generalization of the Sturm–Liouville problem. Completeness of a set of these eigenfunctions in class $C$ is proved. It is shown that in $2+1$ and $3+1$-dimensional Minkowski spaces all these motions reduce to an uniform rotation of a straight string or some such spatially coincident strings (world surface is helicoid). In spaces with higher dimensionality other non-trivial motions of the investigated type are possible. 
@article{TMF_1996_109_2_a2,
     author = {V. P. Petrov and G. S. Sharov},
     title = {Classification of motions of a~relativistic string with massive ends with linearizable boundary conditions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {187--201},
     publisher = {mathdoc},
     volume = {109},
     number = {2},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1996_109_2_a2/}
}
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V. P. Petrov; G. S. Sharov. Classification of motions of a~relativistic string with massive ends with linearizable boundary conditions. Teoretičeskaâ i matematičeskaâ fizika, Tome 109 (1996) no. 2, pp. 187-201. http://geodesic.mathdoc.fr/item/TMF_1996_109_2_a2/