Аннотация:
A trajectory isomorphism between the two Newtonian fixed center problem in the sphere and two associated planar two fixed center problems is constructed by performing two simultaneous gnomonic projections in S2. This isomorphism converts the original quadratures into elliptic integrals and allows the bifurcation diagram of the spherical problem to be analyzed in terms of the corresponding ones of the planar systems. The dynamics along the orbits in the different regimes for the problem in S2 is expressed in terms of Jacobi elliptic functions.
The authors thank the Spanish Ministerio de Economía y Competitividad (MINECO) for financial support under grant MTM2014-57129-C2-1-P and the Junta de Castilla y León grant VA057U16.
Поступила в редакцию: 04.04.2017 Принята в печать: 18.08.2017
Образец цитирования:
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
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\by Miguel A. Gonzalez Leon, Juan Mateos Guilarte, Marina de la Torre Mayado
\paper Orbits in the Problem of Two Fixed Centers on the Sphere
\jour Regul. Chaotic Dyn.
\yr 2017
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\issue 5
\pages 520--542
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\crossref{https://doi.org/10.1134/S1560354717050045}
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Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd273
https://www.mathnet.ru/rus/rcd/v22/i5/p520
Эта публикация цитируется в следующих 6 статьяx:
J F Cariñena, Eduardo Martínez, Miguel C Muñoz-Lecanda, “Sundman transformation and alternative tangent structures”, J. Phys. A: Math. Theor., 56:18 (2023), 185202
A. P. Veselov, Y. Ye, “New integrable two-centre problem on sphere in dirac magnetic field”, Lett. Math. Phys., 110:11 (2020), 3105–3119
M. A. Gonzalez Leon, J. Mateos Guilarte, M. Torre Mayado, “Electron-positron planar orbits in a constant magnetic field”, Physica D, 404 (2020), 132349
E. A. Malkov, A. A. Bekov, S. B. Momynov, I. B. Beckmuhamedov, D. M. Kurmangaliyev, A. M. Mukametzhan, I. S. Orynqul, “Investigation of two fixed centers problem and Henon-Heiles potential based on the Poincare section”, News Natl. Acad. Sci. Rep. Kazakhstan-Ser. Phys.-Math., 1:329 (2020), 55–61
Miguel A. González León, Juan Mateos Guilarte, Marina de la Torre Mayado, Integrability, Supersymmetry and Coherent States, 2019, 359
F. M. El-Sabaa, M. Hosny, S. K. Zakria, “Bifurcations of Liouville tori of a two fixed center problem”, Astrophys. Space Sci., 363:4 (2018), 77
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