1, Universitetskaya str, 426034 Izhevsk
Udmurt State University
Chernoivan V. A., Mamaev I. S.
The restricted two-body problem and the kepler problem in the constant curvature spaces
1999, vol. 4, no. 2, pp. 112-124
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.