Difference between revisions of "User:Tohline/Math/EQ RadialPulsation02"

Latest revision as of 20:13, 8 March 2017

	<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>
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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-<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 } \biggl( \frac{\xi^2}{\theta}\biggr)
++ (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>
 </tr>
 <tr>
    <td align="center" colspan="2">
-where:&nbsp; &nbsp; <math>~Q(\xi) \equiv  \frac{d\ln\theta}{d\ln\xi}</math>, &nbsp;&nbsp; <math>~\sigma_c^2 \equiv \frac{3\omega^2}{2\pi G\rho_c}</math> &nbsp; &nbsp; and, &nbsp; &nbsp; <math>~\alpha \equiv \biggl(3 - \frac{4}{\gamma_\mathrm{g}}\biggr)</math>
+where:&nbsp; &nbsp; <math>~Q(\xi) \equiv - \frac{d\ln\theta}{d\ln\xi} \, ,</math> &nbsp;&nbsp; <math>~\sigma_c^2 \equiv \frac{3\omega^2}{2\pi G\rho_c} \, ,</math> &nbsp; &nbsp; and, &nbsp; &nbsp; <math>~\alpha \equiv \biggl(3 - \frac{4}{\gamma_\mathrm{g}}\biggr)</math>
    </td>
 </tr>
 </table>