Orbits in the problem of two fixed centers on the sphere
| Autor: | Juan Mateos Guilarte, Marina de la Torre Mayado, Miguel Ángel González León |
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| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
FOS: Physical sciences
Center (group theory) Bifurcation diagram 01 natural sciences Gnomonic projection Mathematics (miscellaneous) Planar 0103 physical sciences Elliptic integral 010306 general physics Exactly Solvable 010303 astronomy & astrophysics Trajectory (fluid mechanics) Mathematics Integrable Systems Nonlinear Sciences - Exactly Solvable and Integrable Systems Mechanical Engineering Applied Mathematics Mathematical analysis Statistical and Nonlinear Physics Mathematical Physics (math-ph) Jacobi elliptic functions Modeling and Simulation Mathematical physics Isomorphism Exactly Solvable and Integrable Systems (nlin.SI) |
| Zdroj: | UVaDOC. Repositorio Documental de la Universidad de Valladolid instname GREDOS. Repositorio Institucional de la Universidad de Salamanca |
| Popis: | 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. Comment: Revised version with minor changes and references added. 29 pages, 25 figures |
| Databáze: | OpenAIRE |
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