Аннотация:
In this paper, we consider in detail the 2-body problem in spaces of constant positive
curvature $S^2$ and $S^3$. We perform a reduction (analogous to that in rigid body dynamics) after
which the problem reduces to analysis of a two-degree-of-freedom system. In the general case,
in canonical variables the Hamiltonian does not correspond to any natural mechanical system.
In addition, in the general case, the absence of an analytic additional integral follows from the
constructed Poincaré section. We also give a review of the historical development of celestial
mechanics in spaces of constant curvature and formulate open problems.
Ключевые слова:
celestial mechanics, space of constant curvature, reduction, rigid body dynamics, Poincaré section.
Образец цитирования:
Alexey V. Borisov, Ivan S. Mamaev, Ivan A. Bizyaev, “The Spatial Problem of 2 Bodies on a Sphere. Reduction and Stochasticity”, Regul. Chaotic Dyn., 21:5 (2016), 556–580
\RBibitem{BorMamBiz16}
\by Alexey V. Borisov, Ivan S. Mamaev, Ivan A. Bizyaev
\paper The Spatial Problem of 2 Bodies on a Sphere. Reduction and Stochasticity
\jour Regul. Chaotic Dyn.
\yr 2016
\vol 21
\issue 5
\pages 556--580
\mathnet{http://mi.mathnet.ru/rcd205}
\crossref{https://doi.org/10.1134/S1560354716050075}
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Цитирование в формате AMSBIB
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