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Эта публикация цитируется в 12 научных статьях (всего в 12 статьях)
The Spatial Problem of 2 Bodies on a Sphere. Reduction and Stochasticity
Alexey V. Borisov, Ivan S. Mamaev, Ivan A. Bizyaev
Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
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
| Финансовая поддержка |
Номер гранта |
Российский научный фонд  |
14-50-00005 |
| This work was supported by the Russian Scientific Foundation (project No. 14–50–00005). |
DOI:
https://doi.org/10.1134/S1560354716050075
 Список литературы:
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Тип публикации:
Статья
MSC: 70F15, 01A85
Поступила в редакцию: 17.08.2016
Принята в печать:13.09.2016
Язык публикации: английский
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
Цитирование в формате AMSBIB
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\pages 556--580
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Образцы ссылок на эту страницу:
http://mi.mathnet.ru/rcd205 http://mi.mathnet.ru/rus/rcd/v21/i5/p556
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
Эта публикация цитируется в следующих статьяx:
-
A. V. Borisov, I. S. Mamaev, “Rigid body dynamics in non-euclidean spaces”, Russ. J. Math. Phys., 23:4 (2016), 431–454
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Miguel A. Gonzalez Leon, Juan Mateos Guilarte, Marina de la Torre Mayado, “Orbits in the Problem of Two Fixed Centers on the Sphere”, Regul. Chaotic Dyn., 22:5 (2017), 520–542
 -
A. A. Oshemkov, P. E. Ryabov, S. V. Sokolov, “Explicit determination of certain periodic motions of a generalized two-field gyrostat”, Russ. J. Math. Phys., 24:4 (2017), 517–525
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A. V. Borisov, L. C. Garcia-Naranjo, I. S. Mamaev, J. Montaldi, “Reduction and relative equilibria for the two-body problem on spaces of constant curvature”, Celest. Mech. Dyn. Astron., 130:6 (2018), 43
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Barry K. Carpenter, Gregory S. Ezra, Stavros C. Farantos, Zeb C. Kramer, Stephen Wiggins, “Dynamics on the Double Morse Potential: A Paradigm for Roaming Reactions with no Saddle Points”, Regul. Chaotic Dyn., 23:1 (2018), 60–79
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Jaime Andrade, Claudio Vidal, “Stability of the Polar Equilibria in a Restricted Three-body Problem on the Sphere”, Regul. Chaotic Dyn., 23:1 (2018), 80–101
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A. J. Maciejewski, M. Przybylska, “Dynamics of constrained many body problems in constant curvature two-dimensional manifolds”, Philos. Trans. R. Soc. A-Math. Phys. Eng. Sci., 376:2131 (2018), 20170425
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Philip Arathoon, “Singular Reduction of the $2$-Body Problem on the $3$-Sphere and the $4$-Dimensional Spinning Top”, Regul. Chaotic Dyn., 24:4 (2019), 370–391
-
A. Albouy, L. Zhao, “Lambert's theorem and projective dynamics”, Philos. Trans. R. Soc. A-Math. Phys. Eng. Sci., 377:2158 (2019), 20180417
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D. G. Dritschel, “Point mass dynamics on spherical hypersurfaces”, Philos. Trans. R. Soc. A-Math. Phys. Eng. Sci., 377:2158 (2019), 20180349
-
E. Perez-Chavela, J. M. Sanchez-Cerritos, “Regularization of the restricted (n+1)-body problem on curved spaces”, Astrophys. Space Sci., 364:10 (2019), 170
-
W. Szuminski, “On certain integrable and superintegrable weight-homogeneous Hamiltonian systems”, Commun. Nonlinear Sci. Numer. Simul., 67 (2019), 600–616
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