Template:Math/EQ RadialPulsation04: Difference between revisions

Latest revision as of 17:10, 8 September 2021

	$0 = \frac{d^{2} x}{d r_{0}^{2}} + \frac{1}{r_{0}} [4 + \frac{d \ln P_{0}}{d \ln r_{0}}] \frac{d x}{d r_{0}} + [(3 - \frac{4}{γ_{g}}) \frac{d \ln P_{0}}{d \ln r_{0}}] \frac{x}{r_{0}^{2}} - \frac{1}{Δ} [\frac{d \ln P_{0}}{d \ln r_{0}} \cdot \frac{ρ_{c}}{ρ_{0}} (\frac{σ_{c}^{2}}{6 γ_{g}})] \frac{x}{r_{0}^{2}}$
where: $Δ \equiv \frac{M_{r}}{4 π r_{0}^{3} ρ_{0}},$ $σ_{c}^{2} \equiv \frac{3 ω^{2}}{2 π G ρ_{c}}$

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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[ \alpha \cdot \frac{d\ln P_0}{d\ln r_0} \biggr] \frac{x}{r_0^2}
++ \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}
 </math>
@@ Line 14: / Line 14: @@
 <tr>
    <td align="center" colspan="2">
-where:&nbsp; &nbsp; <math>\Delta \equiv \frac{M_r}{4\pi r_0^3 \rho_0} \, ,</math> &nbsp;&nbsp; <math>\sigma_c^2 \equiv \frac{3\omega^2}{2\pi G\rho_c} \, ,</math>
+where:&nbsp; &nbsp; <math>\Delta \equiv \frac{M_r}{4\pi r_0^3 \rho_0} \, ,</math> &nbsp;&nbsp; <math>\sigma_c^2 \equiv \frac{3\omega^2}{2\pi G\rho_c} </math>
    </td>
 </tr>
 </table>