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The restricted two-body problem and the Kepler problem in the constant curvature spaces. (English) Zbl 1137.70339
Summary: In this work we carry out the bifurcation analysis of the Kepler problem on \(S^3\) and \(L^3\), and construct the analogues of Delaunay variables. We consider the problem of motion of a mass point in the field of moving Newtonian center on \(S^2\) and \(L^2\). The perihelion deviation is derived by the method of perturbation theory under the small curvature, and a numerical investigation is made, using the anologuous problem with rigid body dynamics.

70F05 Two-body problems
37N05 Dynamical systems in classical and celestial mechanics
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