Template:Math/EQ RadialPulsation04 - Revision history

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link=Appendix/EquationTemplates#Stability:_Radial_Pulsation $0 = \frac{d^2x}{dr_0^2} + \frac{1}{r_0}\biggl[4 + \frac{d\ln P_0}{d\ln r_0} \biggr] \frac{dx}{dr_0} + \biggl[ \biggl(3 - \frac{4}{\gamma_g}\biggr) \frac{d\ln P_0}{d\ln r_0} \biggr] \frac{x}{r_0^2} - \frac{1}{\Delta} \biggl[\frac{d\ln P_0}{d\ln r_0}\cdot \frac{\rho_c}{\rho_0} \biggl( \frac{\sigma_c..."$
2023-12-12T20:19:35Z

Created page with "<table border=0 cellpadding=2> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Stability:_Radial_Pulsation </td> <td align="center"> <math>0 = \frac{d^2x}{dr_0^2} + \frac{1}{r_0}\biggl[4 + \frac{d\ln P_0}{d\ln r_0} \biggr] \frac{dx}{dr_0} + \biggl[ \biggl(3 - \frac{4}{\gamma_g}\biggr) \frac{d\ln P_0}{d\ln r_0} \biggr] \frac{x}{r_0^2} - \frac{1}{\Delta} \biggl[\frac{d\ln P_0}{d\ln r_0}\cdot \frac{\rho_c}{\rho_0} \biggl( \frac{\sigma_c..."

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[[Image:LSUkey.png|25px|link=Appendix/EquationTemplates#Stability:_Radial_Pulsation]]
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<math>0 =
\frac{d^2x}{dr_0^2} + \frac{1}{r_0}\biggl[4 + \frac{d\ln P_0}{d\ln r_0} \biggr] \frac{dx}{dr_0}
+ \biggl[ \biggl(3 - \frac{4}{\gamma_g}\biggr) \frac{d\ln P_0}{d\ln r_0} \biggr] \frac{x}{r_0^2}
- \frac{1}{\Delta} \biggl[\frac{d\ln P_0}{d\ln r_0}\cdot \frac{\rho_c}{\rho_0} \biggl( \frac{\sigma_c^2}{6\gamma_g}\biggr)\biggr] \frac{x}{r_0^2}
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where:    <math>\Delta \equiv \frac{M_r}{4\pi r_0^3 \rho_0} \, ,</math>    <math>\sigma_c^2 \equiv \frac{3\omega^2}{2\pi G\rho_c} </math>
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