Curl

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[edit] Discussion

To be written.

[edit] Physical Interpretation

To be written.

[edit] In Orthogonal Curvilinear Coordinates

Where $h i$ is the ith scale factor, the curl may be written as

$\frac{1}{h_1 h_2 h_3} \left|{\begin{bmatrix} h_1 \mathbf{\hat{q}_1} & h_2 \mathbf{\hat{h}_2} & h_3 \mathbf{\hat{q}_3} \\ \\ {\frac{\partial}{\partial q_1}} & {\frac{\partial}{\partial q_2}} & {\frac{\partial}{\partial q_3}} \\ \\ h_1 F_1 & h_2 F_2 & h_3 F_3 \end{bmatrix}}\right|$

as can be swiftly proven using the chain rule.

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Category: Vector Derivatives