User:Tohline/ThreeDimensionalConfigurations/EFE Energies

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Whitworth's (1981) Isothermal Free-Energy Surface
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Properties of Homogeneous Ellipsoids (2)

Relevant Energy Components

As has been explicitly demonstrated in Chapter 3 of EFE and summarized in Table 2-2 (p. 57) of BT87, for an homogeneous ellipsoid this volume integral can be evaluated analytically in closed form. Specifically, at an internal point or on the surface of an homogeneous ellipsoid with semi-axes <math>~(x,y,z) = (a_1,a_2,a_3)</math>,

<math> ~\Phi(\vec{x}) = -\pi G \rho \biggl[ I_\mathrm{BT} a_1^2 - \biggl(A_1 x^2 + A_2 y^2 +A_3 z^2 \biggr) \biggr], </math>

[ EFE, Chapter 3, Eq. (40)1,2 ]
[ BT87, Chapter 2, Table 2-2 ]

where,


See Also


Whitworth's (1981) Isothermal Free-Energy Surface

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