User:Tohline/ThreeDimensionalConfigurations/EFE Energies
|
|---|
| | Tiled Menu | Tables of Content | Banner Video | Tohline Home Page | |
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
|
|
|---|
|
© 2014 - 2021 by Joel E. Tohline |