The Dynamics of Rings: From Benzene to Saturn
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Charles Jaffé [1]
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[1] West Virginia University
West Virginia University
Estados Unidos
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- Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 12, Nº 1, 2013, págs. 89-99
- Idioma: inglés
- Texto completo no disponible (Saber más ...)
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Resumen
In this paper I draw the connection between the chemist’s analysis of the vibrational dynamics of benzene and the analysis of dynamics of celestial rings. Chief among the results is the identification of the hip-hop orbit as the B1g out-of-plane ring mode of benzene. Three additional periodic orbits are predicted to occur. These correspond to the A1g breathing mode and the B1u and B2g in-plane ring modes. These last two are seen to be analogous to out-of-plane hip-hop orbit. The doubly-degenerate modes, E1u, E2u, E2g give rise to one-parameter families of period orbits. These are also discussed. And finally the implications of these results for models of the rings of Saturn are also discussed.
