Commit adecd0ab authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent 2aad2891
Pipeline #19531 canceled with stage
......@@ -22,20 +22,23 @@ visible: false
<br>**$`\boldsymbol{\mathbf{div\,\overrightarrow{X}\,\color{gray}{=\,\dfrac{d\Phi_X}{d\tau}}\,=\,\dfrac{1}{\rho}\;\dfrac{\partial\,(\,\rho\,X_{\rho})}{\partial\,\rho}
+\dfrac{1}{\rho}\;\dfrac{\partial\,X_{\varphi}}{\partial\,\varphi}+\dfrac{\partial\,X_{z}}{\partial\,z}}}`$**
<!--
<br>**$`div\,\overrightarrow{X}\;\color{gray}{=\;\dfrac{d\Phi_X}{d\tau}}\;=\;\dfrac{1}{\rho}\;\dfrac{\partial\,(\,\rho\,X_{\rho})}{\partial\,\rho}
+\dfrac{1}{\rho}\;\dfrac{\partial\,X_{\varphi}}{\partial\,\varphi}+\dfrac{\partial\,X_{z}}{\partial\,z}`$**
-->
##### Expression de la divergence en coordonnées sphériques
<br>**$`\mathbf{\boldsymbol{div\,\overrightarrow{X}\color{gray}{\;=\dfrac{d\Phi_X}{d\tau}}\,=
\; \dfrac{1}{r^2}\;\dfrac{\partial\,(r^2\,X_r}{\partial\,r)}}}`$**
**$`\hspace{3cm}\mathbf{\boldsymbol{+ \dfrac{1}{r\,sin\,\theta}\;\dfrac{\partial\,(sin\,\theta\,X_{\theta})}{\partial\,\theta}}}`$**
**$`\hspace{4cm}\mathbf{\boldsymbol{+ \dfrac{1}{r\,sin\,\theta}\;\dfrac{\partial\,(sin\,\theta\,X_{\theta})}{\partial\,\theta}}}`$**
**$`\hspace{5cm}\mathbf{\boldsymbol{+ \dfrac{1}{r\,sin\,\theta}\;\dfrac{\partial\,X_{\varphi}}{\partial\,\varphi}}}`$**
**$`\hspace{5.5cm}\mathbf{\boldsymbol{+ \dfrac{1}{r\,sin\,\theta}\;\dfrac{\partial\,X_{\varphi}}{\partial\,\varphi}}}`$**
<!--
<br>**$`\mathbf{\boldsymbol{\begin{align}
div\,\overrightarrow{X}\color{gray}{\;=\dfrac{d\Phi_X}{d\tau}}\,=\; &\dfrac{1}{r^2}\;\dfrac{\partial\,(r^2\,X_r}{\partial\,r)}\\
& \quad\quad + \dfrac{1}{r\,sin\,\theta}\;\dfrac{\partial\,(sin\,\theta\,X_{\theta})}{\partial\,\theta}\\
& \quad\quad\quad\quad\quad + \dfrac{1}{r\,sin\,\theta}\;\dfrac{\partial\,X_{\varphi}}{\partial\,\varphi}\end{align}}}`$**
-->
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