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ЖУРНАЛЫ // Regular and Chaotic Dynamics // Архив

Regul. Chaotic Dyn., 1999, том 4, выпуск 2, страницы 112–124 (Mi rcd905)

Эта публикация цитируется в 9 статьях

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

Аннотация: 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.

MSC: 70F07, 70F15, 70F35

Поступила в редакцию: 22.07.1999

Язык публикации: английский

DOI: 10.1070/RD1999v004n02ABEH000107



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