Difference between revisions of "User:Tohline/Apps/DysonWongTori"

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* [http://adsabs.harvard.edu/abs/1965ApJS...11..167O J. Ostriker (1965, ApJ Supplements, 11, 167)] — ''Cylindrical Emden and Associated Functions''
* [http://adsabs.harvard.edu/abs/1965ApJS...11..167O J. Ostriker (1965, ApJ Supplements, 11, 167)] — ''Cylindrical Emden and Associated Functions''
* [http://adsabs.harvard.edu/abs/1942ApJ....95...88R Gunnar Randers (1942, ApJ, 95, 88)] — ''The Equilibrium and Stability of Ring-Shaped 'barred SPIRALS'.''
* [http://adsabs.harvard.edu/abs/1942ApJ....95...88R Gunnar Randers (1942, ApJ, 95, 88)] — ''The Equilibrium and Stability of Ring-Shaped 'barred SPIRALS'.''
* [http://adsabs.harvard.edu/abs/1893RSPTA.184.1041D F. W. Dyson (1893, Philosophical Transaction of the Royal Society London. A., 184, 1041 - 1106)] — ''The Potential of an Anchor Ring. Part II.'' (interior gravitational potential)
* [http://adsabs.harvard.edu/abs/1893RSPTA.184.1041D F. W. Dyson (1893, Philosophical Transaction of the Royal Society London. A., 184, 1041 - 1106)] &#8212; ''The Potential of an Anchor Ring. Part II.'' <ol type="a"><li>In this paper, Dyson derives the gravitational potential ''inside'' the ring mass distribution</li></ol>
* [http://adsabs.harvard.edu/abs/1893RSPTA.184...43D F. W. Dyson (1893, Philosophical Transaction of the Royal Society London. A., 184, 43 - 95)] &#8212; ''The Potential of an Anchor Ring. Part I.'' (exterior gravitational potential)
* [http://adsabs.harvard.edu/abs/1893RSPTA.184...43D F. W. Dyson (1893, Philosophical Transaction of the Royal Society London. A., 184, 43 - 95)] &#8212; ''The Potential of an Anchor Ring. Part I.''<ol type="a"><li>In this paper, Dyson derives the gravitational potential ''exterior to'' the ring mass distribution</li></ol>
* [http://adsabs.harvard.edu/abs/1885AN....111...37K S. Kowalewsky (1885, Astronomische Nachrichten, 111, 37)] &#8212; ''Zus&auml;tze und Bemerkungen zu Laplace's Untersuchung &uuml;ber die Gestalt der Saturnsringe''
* [http://adsabs.harvard.edu/abs/1885AN....111...37K S. Kowalewsky (1885, Astronomische Nachrichten, 111, 37)] &#8212; ''Zus&auml;tze und Bemerkungen zu Laplace's Untersuchung &uuml;ber die Gestalt der Saturnsringe''
* Poincar&eacute; (1885a, C. R. Acad. Sci., 100, 346), (1885b, Bull. Astr., 2, 109), (1885c, Bull. Astr. 2, 405). &#8212; references copied from paper by [http://adsabs.harvard.edu/abs/1974ApJ...190..675W Wong (1974)]
* Poincar&eacute; (1885a, C. R. Acad. Sci., 100, 346), (1885b, Bull. Astr., 2, 109), (1885c, Bull. Astr. 2, 405). &#8212; references copied from paper by [http://adsabs.harvard.edu/abs/1974ApJ...190..675W Wong (1974)]

Revision as of 14:32, 11 August 2017

Self-Gravitating, Incompressible (Dyson-Wong) Tori

Much of the introductory material of this chapter has been drawn from the paper by Tohline & Hachisu (1990) titled, The Breakup of Self-Gravitating Rings, Tori, and Accretion Disks.

Whitworth's (1981) Isothermal Free-Energy Surface
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Overview

In his pioneering work, F. W. Dyson (1893, Philosophical Transactions of the Royal Society of London. A., 184, 43 - 95) and (1893, Philosophical Transactions of the Royal Society of London. A., 184, 1041 - 1106) used analytic techniques to determine the approximate equilibrium structure of axisymmetric, uniformly rotating, incompressible tori. C.-Y. Wong (1974, ApJ, 190, 675 - 694) extended Dyson's work, using numerical techniques to obtain more accurate — but still approximate — equilibrium structures for incompressible tori having solid body rotation. Since then, Y. Eriguchi & D. Sugimoto (1981, Progress of Theoretical Physics, 65, 1870 - 1875) and I. Hachisu, J. E. Tohline & Y. Eriguchi (1987, ApJ, 323, 592 - 613) have mapped out the full sequence of Dyson-Wong tori, beginning from a bifurcation point on the Maclaurin spheroid sequence.

See Also

  1. Shortly after their equation (3.2), Marcus, Press & Teukolsky make the following statement: "… we know that an equilibrium incompressible configuration must rotate uniformly on cylinders (the famous "Poincaré-Wavre" theorem, cf. Tassoul 1977, &Sect;4.3) …"


 

Whitworth's (1981) Isothermal Free-Energy Surface

© 2014 - 2021 by Joel E. Tohline
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Recommended citation:   Tohline, Joel E. (2021), The Structure, Stability, & Dynamics of Self-Gravitating Fluids, a (MediaWiki-based) Vistrails.org publication, https://www.vistrails.org/index.php/User:Tohline/citation