Editing SSC/Stability/n5PolytropeLAWE (section)

=Related Discussions=
* Radial Oscillations of [[SSC/Stability/UniformDensity#The_Stability_of_Uniform-Density_Spheres|Uniform-density sphere]]
* Radial Oscillations of Isolated Polytropes
** [[SSC/Stability/Polytropes#Radial_Oscillations_of_Polytropic_Spheres|Setup]]
** n = 1:&nbsp; [[SSC/Stability/n1PolytropeLAWE|Attempt at Formulating an Analytic Solution]]
** n = 3:&nbsp; [[SSC/Stability/n3PolytropeLAWE|Numerical Solution]] to compare with [http://adsabs.harvard.edu/abs/1941ApJ....94..245S M. Schwarzschild (1941)]
** n = 5:&nbsp; [[SSC/Stability/n5PolytropeLAWE|Attempt at Formulating an Analytic Solution]]

* In an accompanying [[Appendix/Ramblings/SphericalWaveEquation#Playing_With_Spherical_Wave_Equation|Chapter within our "Ramblings" Appendix]], we have played with the adiabatic wave equation for polytropes, examining its form when the primary perturbation variable is an enthalpy-like quantity, rather than the radial displacement of a spherical mass shell.  This was done in an effort to mimic the approach that has been taken in studies of the [[Apps/ImamuraHadleyCollaboration#Papaloizou-Pringle_Tori|stability of Papaloizou-Pringle tori]].

* <math>~n=3</math> &hellip; [http://adsabs.harvard.edu/abs/1941ApJ....94..245S M. Schwarzschild (1941, ApJ, 94, 245)], ''Overtone Pulsations of the Standard Model'':  This work is referenced in &sect;38.3 of [<b>[[Appendix/References#KW94|<font color="red">KW94</font>]]</b>].  It contains an analysis of the radial modes of oscillation of <math>~n=3</math> polytropes, assuming various values of the adiabatic exponent.

* <math>~n=2</math> &hellip; [http://adsabs.harvard.edu/abs/1961MNRAS.122..409P C. Prasad &amp; H. S. Gurm (1961, MNRAS, 122, 409)], ''Radial Pulsations of the Polytrope, n = 2''

* <math>~n=\tfrac{3}{2}</math> &hellip;  D. Lucas (1953, Bul. Soc. Roy. Sci. Liege, 25, 585) &hellip; Citation obtained from the Prasad &amp; Gurm (1961) article.

* <math>~n=1</math> &hellip;  L. D. Chatterji (1951, Proc. Nat. Inst. Sci. [India], 17, 467) &hellip; Citation obtained from the Prasad &amp; Gurm (1961) article.

* Composite Polytropes &hellip; [http://adsabs.harvard.edu/abs/1968MNRAS.140..235S M. Singh (1968, MNRAS, 140, 235-240)], ''Effect of Central Condensation on the Pulsation Characteristics''

* Summary of Known Analytic Solutions &hellip; [http://adsabs.harvard.edu/abs/1981MNRAS.197..351S R. Stothers (1981, MNRAS, 197, 351-361)], ''Analytic Solutions of the Radial Pulsation Equation for Rotating and Magnetic Star Models''

* Interesting Composite! &hellip; [http://adsabs.harvard.edu/abs/1948MNRAS.108..414P C. Prasad (1948, MNRAS, 108, 414-416)], ''Radial Oscillations of a Particular Stellar Model''

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