The restricted two-body problem in constant curvature spaces

Details The restricted two-body problem in constant curvature spaces The restricted two-body problem in constant curvature spaces

2005-07-26

arxiv.org/abs/nlin/0507056v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

29 pages, 7 figures

Scientific paper

10.1007/s10569-006-9012-2

We perform the bifurcation analysis of the Kepler problem on $S^3$ and $L^3$. An analogue of the Delaunay variables is introduced. We investigate the motion of a point mass in the field of the Newtonian center moving along a geodesic on $S^2$ and $L^2$ (the restricted two-body problem). When the curvature is small, the pericenter shift is computed using the perturbation theory. We also present the results of the numerical analysis based on the analogy with the motion of rigid body.

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