Toroidal coordinates: Difference between revisions

Toroidal coordinates (view source)

4 bytes added , 17 August 2010

204

edits

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 Some useful properties of the FSA are
-:<math>	\langle\nabla\cdot\Gamma\rangle = \frac{d}{dV}\langle\Gamma\cdot\nabla V\rangle  = \frac{1}{V'}\frac{d}{d\psi}V'\langle\Gamma\cdot\nabla \psi\rangle</math>
+* <math>	\langle\nabla\cdot\Gamma\rangle = \frac{d}{dV}\langle\Gamma\cdot\nabla V\rangle  = \frac{1}{V'}\frac{d}{d\psi}V'\langle\Gamma\cdot\nabla \psi\rangle</math>
-:<math> \int_{V}\nabla\cdot\Gamma\; dV =  \langle\Gamma\cdot\nabla V\rangle = V'\langle\Gamma\cdot\nabla \psi\rangle</math>
+* <math> \int_{V}\nabla\cdot\Gamma\; dV =  \langle\Gamma\cdot\nabla V\rangle = V'\langle\Gamma\cdot\nabla \psi\rangle</math>
-:<math>	\langle \mathbf{B}\cdot\nabla f \rangle = 0~,\qquad \forall~ \mathrm{single~valued~} f, ~ \mathrm{if}~ \nabla\cdot\mathbf{B} = 0 ~\mathrm{and}~ \nabla V\cdot\mathbf{B} = 0 </math>
+* <math>	\langle \mathbf{B}\cdot\nabla f \rangle = 0~,\qquad \forall~ \mathrm{single~valued~} f, ~ \mathrm{if}~ \nabla\cdot\mathbf{B} = 0 ~\mathrm{and}~ \nabla V\cdot\mathbf{B} = 0 </math>
-:<math> \langle \sqrt{g}^{-1}\rangle = \frac{4\pi^2}{V'}
+* <math> \langle \sqrt{g}^{-1}\rangle = \frac{4\pi^2}{V'}
 </math>