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Flux coordinates: Difference between revisions
→Gradient, Divergence and Curl in curvilinear coordinates
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\nabla f = \frac{\partial f}{\partial u^i}\nabla u^i = \frac{\partial f}{\partial u^i}\mathbf{e}^i~. | \nabla f = \frac{\partial f}{\partial u^i}\nabla u^i = \frac{\partial f}{\partial u^i}\mathbf{e}^i~. | ||
</math> | </math> | ||
The divergence of a vector \mathbf{A} is best expressed in terms of its contravariant components | The divergence of a vector <math>\mathbf{A}</math> is best expressed in terms of its contravariant components | ||
:<math> | :<math> | ||
\nabla\cdot\mathbf{A} = \frac{1}{\sqrt{g}}\frac{\partial}{\partial u^i}(\sqrt{g}A^i)~, | \nabla\cdot\mathbf{A} = \frac{1}{\sqrt{g}}\frac{\partial}{\partial u^i}(\sqrt{g}A^i)~, | ||