Difference between revisions of "User:Tohline/Math/EQ RadialPulsation02"
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(Created page with '<table border=0 cellpadding=2> <tr> <td align="right"> [[Image:LSU_Key.png|25px|link=http://www.vistrails.org/index.php/User:Tohline/Appendix/Equation_templates#Stability:__Radia…') |
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<math>~0 = \frac{d^2x}{d\xi^2} + \biggl[ 4 + (n+1) Q \biggr] \frac{1}{\xi} \cdot \frac{dx}{d\xi} | <math>~0 = \frac{d^2x}{d\xi^2} + \biggl[ 4 + (n+1) Q \biggr] \frac{1}{\xi} \cdot \frac{dx}{d\xi} | ||
+ (n+1) \biggl[\frac{\sigma_c^2}{6\gamma_g } \ | + (n+1) \biggl[ \biggl( \frac{\sigma_c^2}{6\gamma_g } \biggr) \frac{\xi^2}{\theta} | ||
+ \alpha Q\biggr] \frac{x}{\xi^2} </math> | + \alpha Q\biggr] \frac{x}{\xi^2} </math> | ||
</td> | </td> | ||
Revision as of 20:06, 8 March 2017
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<math>~0 = \frac{d^2x}{d\xi^2} + \biggl[ 4 + (n+1) Q \biggr] \frac{1}{\xi} \cdot \frac{dx}{d\xi} + (n+1) \biggl[ \biggl( \frac{\sigma_c^2}{6\gamma_g } \biggr) \frac{\xi^2}{\theta} + \alpha Q\biggr] \frac{x}{\xi^2} </math> |
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where: <math>~Q(\xi) \equiv \frac{d\ln\theta}{d\ln\xi}</math>, <math>~\sigma_c^2 \equiv \frac{3\omega^2}{2\pi G\rho_c}</math> and, <math>~\alpha \equiv \biggl(3 - \frac{4}{\gamma_\mathrm{g}}\biggr)</math> |
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