Geodesic
Formulation of the relativistic mechanics of systems of interacting particles
Teoretičeskaâ i matematičeskaâ fizika, Tome 46 (1981) no. 1, pp. 50-63

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A Poincaré invariant formulation of classical relativistic mechanics of a system of $n$ interacting particles is given. The equations of motion are the equations of the characteristics of a Pfaffian form, which relates the action element to the elements of the $4n$ coordinates of the system. The characteristics are found on a subsurface defined by $n$ constraints, which include the particle masses. A canonical transformation to collective variables for two particles is found, this satisfying the conditions of covarianee and the correct nonrelativistic limit. The action satisfies $n$ Hamilton–Jacobi equations. The scattering of two particles is considered. The nonuniqueness of the worldlines of the particles in the interaction region is discussed. 
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     author = {N. P. Klepikov and A. N. Shatnii},
     title = {Formulation of the relativistic mechanics of systems of interacting particles},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     year = {1981},
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N. P. Klepikov; A. N. Shatnii. Formulation of the relativistic mechanics of systems of interacting particles. Teoretičeskaâ i matematičeskaâ fizika, Tome 46 (1981) no. 1, pp. 50-63. http://geodesic.mathdoc.fr/item/TMF_1981_46_1_a4/