Geodesic
Two-body problem on spaces of constant curvature: I. Dependence of the Hamiltonian on the symmetry group and the reduction of the classical system
Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 2, pp. 249-264 
A. V. Shchepetilov. Two-body problem on spaces of constant curvature: I. Dependence of the Hamiltonian on the symmetry group and the reduction of the classical system. Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 2, pp. 249-264. http://geodesic.mathdoc.fr/item/TMF_2000_124_2_a4/
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     author = {A. V. Shchepetilov},
     title = {Two-body problem on spaces of constant curvature: {I.~Dependence} of the {Hamiltonian} on the symmetry group and the reduction of the classical system},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {249--264},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2000_124_2_a4/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the problem of two bodies with central interaction that propagate in a simply connected space with a constant curvature and an arbitrary dimension. We obtain the explicit expression for the quantum Hamiltonian via the radial differential operator and generators of the isometry group of a configuration space. We describe the reduced classical mechanical system determined on the homogeneous space of a Lie group in terms of orbits of the coadjoint representation of this group. We describe the reduced classical two-body problem.

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