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

From VistrailsWiki
Jump to navigation Jump to search
Line 11: Line 11:
===Uniform Rotation===
===Uniform Rotation===


* [https://ui.adsabs.harvard.edu/abs/1923MNRAS..83..118M/abstract E. A. Milne (1923)], MNRAS, 83, 118: ''The Equilibrium of a Rotating Star''
* [https://ui.adsabs.harvard.edu/abs/1924MNRAS..84..665V/abstract H. von Zeipel (1924)], MNRAS, 84, 665: ''The radiative equilibrium of a rotating system of gaseous masses
* [https://ui.adsabs.harvard.edu/abs/1924MNRAS..84..684V/abstract H. von Zeipel (1924)], MNRAS, 84, 684:  ''The radiative equilibrium of a slightly oblate rotating star''
* [https://ui.adsabs.harvard.edu/abs/1962ApJ...136.1069C/abstract S. Chandrasekhar & N. R. Lebovitz (1962)], ApJ, 136, 1069
* [https://ui.adsabs.harvard.edu/abs/1962ApJ...136.1069C/abstract S. Chandrasekhar & N. R. Lebovitz (1962)], ApJ, 136, 1069
<table border="0" align="center" width="100%" cellpadding="1"><tr>
<table border="0" align="center" width="100%" cellpadding="1"><tr>
<td align="center" width="5%">&nbsp;</td><td align="left">
<td align="center" width="5%">&nbsp;</td><td align="left">
<font color="green">If one ''assumes'' that the mass is distributed uniformly, the equilibrium configurations are the well-known Maclaurin spheroids.  This paper will be devoted to finding the oscillation frequencies of the Maclaurin spheroids.</font>
<font color="green">If one ''assumes'' that the mass is distributed uniformly, the equilibrium configurations are the well-known Maclaurin spheroids.  This paper will be devoted to finding the oscillation frequencies of the Maclaurin spheroids.</font>
</td></tr></table>
* [https://ui.adsabs.harvard.edu/abs/1933MNRAS..93..390C/abstract S. Chandrasekhar (1933)], MNRAS, 93, 390
<table border="0" align="center" width="100%" cellpadding="1"><tr>
<td align="center" width="5%">&nbsp;</td><td align="left">
The purpose of this paper is <font color="green">&hellip; to extend Emden's [work] to the case of rotating gas spheres which in their non-rotating states have polytropic distributions described by the so-called Emden functions.  &hellip; the gas sphere is set rotating at a constant small angular velocity <math>~\omega</math>. &hellip; we shall assume that the rotation is so slow that the configurations are only slightly oblate.</font>
</td></tr></table>
</td></tr></table>
* [https://ui.adsabs.harvard.edu/abs/1970A%26A.....4..423T/abstract J. - L. Tassoul &amp; J. P. Ostriker (1970)], Astron. Ap., 4, 423
* [https://ui.adsabs.harvard.edu/abs/1970A%26A.....4..423T/abstract J. - L. Tassoul &amp; J. P. Ostriker (1970)], Astron. Ap., 4, 423
Line 21: Line 29:
===Differential Rotation===
===Differential Rotation===


* [https://ui.adsabs.harvard.edu/abs/1933MNRAS..93..390C/abstract S. Chandrasekhar (1933)], MNRAS, 93, 390
<table border="0" align="center" width="100%" cellpadding="1"><tr>
<td align="center" width="5%">&nbsp;</td><td align="left">
The purpose of this paper is <font color="green">&hellip; to extend Emden's [work] to the case of rotating gas spheres which in their non-rotating states have polytropic distributions described by the so-called Emden functions.  &hellip; the gas sphere is set rotating at a constant small angular velocity <math>~\omega</math>. &hellip; we shall assume that the rotation is so slow that the configurations are only slightly oblate.</font>
</td></tr></table>
* [https://ui.adsabs.harvard.edu/abs/1962ApJ...136.1082C/abstract S. Chandrasekhar &amp; N. R. Lebovitz (1962)], ApJ, 136, 1082
* [https://ui.adsabs.harvard.edu/abs/1962ApJ...136.1082C/abstract S. Chandrasekhar &amp; N. R. Lebovitz (1962)], ApJ, 136, 1082
<table border="0" align="center" width="100%" cellpadding="1"><tr>
<table border="0" align="center" width="100%" cellpadding="1"><tr>

Revision as of 05:09, 16 June 2019

Rotationally Flattened Polytropes

Whitworth's (1981) Isothermal Free-Energy Surface
|   Tiled Menu   |   Tables of Content   |  Banner Video   |  Tohline Home Page   |

Example Equilibrium Configurations

Reviews

Uniform Rotation

 

If one assumes that the mass is distributed uniformly, the equilibrium configurations are the well-known Maclaurin spheroids. This paper will be devoted to finding the oscillation frequencies of the Maclaurin spheroids.

 

The purpose of this paper is … to extend Emden's [work] to the case of rotating gas spheres which in their non-rotating states have polytropic distributions described by the so-called Emden functions. … the gas sphere is set rotating at a constant small angular velocity <math>~\omega</math>. … we shall assume that the rotation is so slow that the configurations are only slightly oblate.

Differential Rotation

 

The oscillations of slowly rotating polytopes are treated in this paper. The initial equilibrium configurations are constructed as in Chandrasekhar (1933).

See Also


Whitworth's (1981) Isothermal Free-Energy Surface

© 2014 - 2021 by Joel E. Tohline
|   H_Book Home   |   YouTube   |
Appendices: | Equations | Variables | References | Ramblings | Images | myphys.lsu | ADS |
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