Geodesic
Reduction of the~two-body problem with central interaction on simply connected surfaces of a~constant curvature
Fundamentalʹnaâ i prikladnaâ matematika, Tome 6 (2000) no. 1, pp. 249-263.

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The problem of two particles with central interaction on simply connected surfaces of a constant curvature was considered. Due to the absence in this case of the Galileo transformation, it's reduction to the one particle problem was carried out by Marsden–Weinstein method. The classification of reduced dynamic systems was given. For two of them the conditions of the global solution existence for dynamic equations with attractive potentials were found. The comparison of the structure of obtained Hamiltonians with integrals of one particle problem with Bertrand's potentials was carried out. 
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     author = {A. V. Shchepetilov},
     title = {Reduction of the~two-body problem with central interaction on simply connected surfaces of a~constant curvature},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {249--263},
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     number = {1},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2000_6_1_a19/}
}
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A. V. Shchepetilov. Reduction of the~two-body problem with central interaction on simply connected surfaces of a~constant curvature. Fundamentalʹnaâ i prikladnaâ matematika, Tome 6 (2000) no. 1, pp. 249-263. http://geodesic.mathdoc.fr/item/FPM_2000_6_1_a19/