The Dynamics of Rings: From Benzene to Saturn

Abstract 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 period...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Jaffé, Charles [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2012

Schlagwörter:	Saturn Benzene Hip-hop Choreographies

Anmerkung:	© Springer Basel AG 2012

Übergeordnetes Werk:	Enthalten in: Qualitative theory of dynamical systems - Basel : Birkhäuser, 1999, 12(2012), 1 vom: 21. Aug., Seite 89-99
Übergeordnetes Werk:	volume:12 ; year:2012 ; number:1 ; day:21 ; month:08 ; pages:89-99

Links:	Volltext

DOI / URN:	10.1007/s12346-012-0088-7

Katalog-ID:	SPR024954357

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520			\|a Abstract 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.
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publishDate	2012
allfields	10.1007/s12346-012-0088-7 doi (DE-627)SPR024954357 (SPR)s12346-012-0088-7-e DE-627 ger DE-627 rakwb eng Jaffé, Charles verfasserin aut The Dynamics of Rings: From Benzene to Saturn 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel AG 2012 Abstract 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. Saturn (dpeaa)DE-He213 Benzene (dpeaa)DE-He213 Hip-hop (dpeaa)DE-He213 Choreographies (dpeaa)DE-He213 Enthalten in Qualitative theory of dynamical systems Basel : Birkhäuser, 1999 12(2012), 1 vom: 21. Aug., Seite 89-99 (DE-627)582026512 (DE-600)2457088-6 1662-3592 nnns volume:12 year:2012 number:1 day:21 month:08 pages:89-99 https://dx.doi.org/10.1007/s12346-012-0088-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 12 2012 1 21 08 89-99
spelling	10.1007/s12346-012-0088-7 doi (DE-627)SPR024954357 (SPR)s12346-012-0088-7-e DE-627 ger DE-627 rakwb eng Jaffé, Charles verfasserin aut The Dynamics of Rings: From Benzene to Saturn 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel AG 2012 Abstract 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. Saturn (dpeaa)DE-He213 Benzene (dpeaa)DE-He213 Hip-hop (dpeaa)DE-He213 Choreographies (dpeaa)DE-He213 Enthalten in Qualitative theory of dynamical systems Basel : Birkhäuser, 1999 12(2012), 1 vom: 21. Aug., Seite 89-99 (DE-627)582026512 (DE-600)2457088-6 1662-3592 nnns volume:12 year:2012 number:1 day:21 month:08 pages:89-99 https://dx.doi.org/10.1007/s12346-012-0088-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 12 2012 1 21 08 89-99
allfields_unstemmed	10.1007/s12346-012-0088-7 doi (DE-627)SPR024954357 (SPR)s12346-012-0088-7-e DE-627 ger DE-627 rakwb eng Jaffé, Charles verfasserin aut The Dynamics of Rings: From Benzene to Saturn 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel AG 2012 Abstract 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. Saturn (dpeaa)DE-He213 Benzene (dpeaa)DE-He213 Hip-hop (dpeaa)DE-He213 Choreographies (dpeaa)DE-He213 Enthalten in Qualitative theory of dynamical systems Basel : Birkhäuser, 1999 12(2012), 1 vom: 21. Aug., Seite 89-99 (DE-627)582026512 (DE-600)2457088-6 1662-3592 nnns volume:12 year:2012 number:1 day:21 month:08 pages:89-99 https://dx.doi.org/10.1007/s12346-012-0088-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 12 2012 1 21 08 89-99
allfieldsGer	10.1007/s12346-012-0088-7 doi (DE-627)SPR024954357 (SPR)s12346-012-0088-7-e DE-627 ger DE-627 rakwb eng Jaffé, Charles verfasserin aut The Dynamics of Rings: From Benzene to Saturn 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel AG 2012 Abstract 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. Saturn (dpeaa)DE-He213 Benzene (dpeaa)DE-He213 Hip-hop (dpeaa)DE-He213 Choreographies (dpeaa)DE-He213 Enthalten in Qualitative theory of dynamical systems Basel : Birkhäuser, 1999 12(2012), 1 vom: 21. Aug., Seite 89-99 (DE-627)582026512 (DE-600)2457088-6 1662-3592 nnns volume:12 year:2012 number:1 day:21 month:08 pages:89-99 https://dx.doi.org/10.1007/s12346-012-0088-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 12 2012 1 21 08 89-99
allfieldsSound	10.1007/s12346-012-0088-7 doi (DE-627)SPR024954357 (SPR)s12346-012-0088-7-e DE-627 ger DE-627 rakwb eng Jaffé, Charles verfasserin aut The Dynamics of Rings: From Benzene to Saturn 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel AG 2012 Abstract 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. Saturn (dpeaa)DE-He213 Benzene (dpeaa)DE-He213 Hip-hop (dpeaa)DE-He213 Choreographies (dpeaa)DE-He213 Enthalten in Qualitative theory of dynamical systems Basel : Birkhäuser, 1999 12(2012), 1 vom: 21. Aug., Seite 89-99 (DE-627)582026512 (DE-600)2457088-6 1662-3592 nnns volume:12 year:2012 number:1 day:21 month:08 pages:89-99 https://dx.doi.org/10.1007/s12346-012-0088-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 12 2012 1 21 08 89-99
language	English
source	Enthalten in Qualitative theory of dynamical systems 12(2012), 1 vom: 21. Aug., Seite 89-99 volume:12 year:2012 number:1 day:21 month:08 pages:89-99
sourceStr	Enthalten in Qualitative theory of dynamical systems 12(2012), 1 vom: 21. Aug., Seite 89-99 volume:12 year:2012 number:1 day:21 month:08 pages:89-99
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Saturn Benzene Hip-hop Choreographies
isfreeaccess_bool	false
container_title	Qualitative theory of dynamical systems
authorswithroles_txt_mv	Jaffé, Charles @@aut@@
publishDateDaySort_date	2012-08-21T00:00:00Z
hierarchy_top_id	582026512
id	SPR024954357
language_de	englisch
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author	Jaffé, Charles
spellingShingle	Jaffé, Charles misc Saturn misc Benzene misc Hip-hop misc Choreographies The Dynamics of Rings: From Benzene to Saturn
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topic_title	The Dynamics of Rings: From Benzene to Saturn Saturn (dpeaa)DE-He213 Benzene (dpeaa)DE-He213 Hip-hop (dpeaa)DE-He213 Choreographies (dpeaa)DE-He213
topic	misc Saturn misc Benzene misc Hip-hop misc Choreographies
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title	The Dynamics of Rings: From Benzene to Saturn
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title_full	The Dynamics of Rings: From Benzene to Saturn
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title_sort	dynamics of rings: from benzene to saturn
title_auth	The Dynamics of Rings: From Benzene to Saturn
abstract	Abstract 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. © Springer Basel AG 2012
abstractGer	Abstract 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. © Springer Basel AG 2012
abstract_unstemmed	Abstract 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. © Springer Basel AG 2012
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title_short	The Dynamics of Rings: From Benzene to Saturn
url	https://dx.doi.org/10.1007/s12346-012-0088-7
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR024954357</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230403054700.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201007s2012 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s12346-012-0088-7</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR024954357</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s12346-012-0088-7-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Jaffé, Charles</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="4"><subfield code="a">The Dynamics of Rings: From Benzene to Saturn</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2012</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer Basel AG 2012</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract 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. 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