The restricted two-body problem and the kepler problem in the constant curvature spaces
1999, Volume 4, Number 2, pp. 112-124
Author(s): Chernoivan V. A., Mamaev I. S.
Author(s): Chernoivan V. A., Mamaev I. S.
In this work we carry out the bifurcation analysis of the Kepler problem on $S^3$ and $L^3$, and construct the analogues of Delaunau 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 anology of this problem with rigid body dynamics.
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