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Эта публикация цитируется в 6 научных статьях (всего в 6 статьях)
Orbits in the Problem of Two Fixed Centers on the Sphere
Miguel A. Gonzalez Leon, Juan Mateos Guilarte, Marina de la Torre Mayado Departamento de Física Fundamental, University of Salamanca, Facultad de Ciencias, Casas del Parque II, 37008 Salamanca, Spain
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 $S^2$. 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 $S^2$ is expressed in terms of Jacobi elliptic functions.
Ключевые слова:
spherical two-center problem, separation of variables, spheroconical coordinates, elliptic coordinates.
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
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd273 https://www.mathnet.ru/rus/rcd/v22/i5/p520
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