On isomorphisms of some integrable systems on a plane and a sphere
2007, Vol. 3, No. 1, pp. 49-56
Author(s): Borisov A. V., Mamaev I. S.
We consider
trajectory isomorphisms between various integrable
systems on an $n$-dimensional sphere $S^n$ and a Euclidean space $R^n$.
Some of the systems are classical integrable problems of Celestial Mechanics
in plane and curved spaces. All the systems under consideration have an additional
first integral quadratic in momentum and can be integrated analytically by using
the separation of variables. We show that
some integrable problems in constant curvature spaces are not essentially new from the viewpoint of the
theory of integration, and they can be analyzed using known results of classical Celestial Mechanics.
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