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The restricted two-body problem in constant curvature spaces. (English) Zbl 1116.70015
Summary: We perform the bifurcation analysis of the Kepler problem on \(\mathbb{S}^{3}\) and \(\mathbb{H}^{3}\). An analog of the Delaunay variables is introduced. We investigate the motion of a point mass in the field of a Newtonian center moving along a geodesic on \(\mathbb{S}^{2}\) and \(\mathbb{H}^{2}\) (the restricted two-body problem). For the case of a small curvature, the pericenter shift is computed using the perturbation theory. We also present the results of numerical analysis based on an analogy with the motion of a rigid body.

70F05 Two-body problems
37J20 Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems
37N05 Dynamical systems in classical and celestial mechanics
70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics
Full Text: DOI
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