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This article is cited in 9 scientific papers (total in 9 papers)
The restricted two-body problem and the Kepler problem in the constant curvature spaces
V. А. Chernoïvan, I. S. Mamaev Laboratory of Dynamical Chaos and Nonlinearity,
Udmurt State University,
Universitetskaya 1, 426034 Izhevsk, Russia
Abstract:
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.
Received: 22.07.1999
Citation:
V. А. Chernoïvan, I. S. Mamaev, “The restricted two-body problem and the Kepler problem in the constant curvature spaces”, Regul. Chaotic Dyn., 4:2 (1999), 112–124
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https://www.mathnet.ru/eng/rcd905 https://www.mathnet.ru/eng/rcd/v4/i2/p112
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Abstract page: | 114 |
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