Geodesic
Example of~relativistic two-body problem.
Teoretičeskaâ i matematičeskaâ fizika, Tome 42 (1980) no. 1, pp. 59-70

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A certain type of interaction of two particles is reduced to the Lagrange system of partial differential equations for the world surface connecting the world lines which are the particle trajectories, the mechanics equations being the boundary conditions. The simplest example of this type, the nonrelativistic model, is analysed. The two-body relativistic problem analogous to the considered nonrelativistic model also belongs to the type under consideration. 
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     author = {N. A. Chernikov and N. S. Shavokhina},
     title = {Example of~relativistic two-body problem.},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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N. A. Chernikov; N. S. Shavokhina. Example of~relativistic two-body problem.. Teoretičeskaâ i matematičeskaâ fizika, Tome 42 (1980) no. 1, pp. 59-70. http://geodesic.mathdoc.fr/item/TMF_1980_42_1_a6/