Electronic Resource
Springer
Celestial mechanics and dynamical astronomy
16 (1977), S. 191-208
ISSN:
1572-9478
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract The main result of this paper is a theorem on the trajectory equivalence of phase flows on isoenergetic surfaces with a positive energy level in the Kepler problem and perturbed kepler problem. The following two facts are crucial for proving it: firstly, an isomorphism of the phase flow on an isoenergetic surface in the Kepler problem and the geodesic flow in a constant curvature space. The isomorphism is studied in detail. In particular, all the integrals of the Kepler problem are obtained proceeding from the group-theory considerations. The second fact is a generalization of the theorem on structural stability of Anosov flows onto non-compact manifolds.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01228600
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