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Principal Governing Equations (PGEs)		Continuity		Euler		1^st Law of Thermodynamics		Poisson

Equation of State (EOS)		Total Pressure

One-Dimensional PGEs

<math>~\frac{1}{\xi^2} \frac{d}{d\xi}\biggl( \xi^2 \frac{d\psi}{d\xi} \biggr) = e^{-\psi}</math>

<math>~\frac{1}{\xi^2} \frac{d}{d\xi}\biggl( \xi^2 \frac{d\Theta_H}{d\xi} \biggr) = - \Theta_H^n</math>

Zero-Temperature White Dwarf		Chandrasekhar Limiting Mass

Pressure-Truncated Configurations		Bonnor-Ebert (Isothermal) Spheres		Polytropes		Equilibrium Sequence Turning-Points

Composite Polytropes (Bipolytropes)		Schönberg- Chandrasekhar Mass		Analytic <math>~(n_c, n_e)</math> = <math>~(5,1)</math>		Analytic <math>~(n_c, n_e)</math> = <math>~(1,5)</math>		Equilibrium Sequence Turning-Points

Radial Pulsation Equation		Example Derivations & Statement of Eigenvalue Problem		Jeans (1928) or Bonnor (1957)		Ledoux & Walraven (1958)		Rosseland (1969)		Relationship to Sound Waves

Uniform-Density Configurations		Sterne's Analytic Sol'n of Eigenvalue Problem

	<math>~0 = \frac{d^2x}{d\xi^2} + \biggl[4 - \xi \biggl( \frac{d\psi}{d\xi} \biggr) \biggr] \frac{1}{\xi} \cdot \frac{dx}{d\xi} + \biggl[ \biggl( \frac{\sigma_c^2}{6\gamma_\mathrm{g}}\biggr)\xi^2 - \alpha \xi \biggl( \frac{d\psi}{d\xi} \biggr) \biggr] \frac{x}{\xi^2} </math>
where: <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>

	<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>