Commit d4759f2c authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent a0af367d
Pipeline #19536 failed with stage
......@@ -53,35 +53,10 @@ $`\overrightarrow{rot}\;\overrightarrow{X_M} \cdot \overrightarrow{e_y}=
##### Expression du rotationnel en coordonnées cartésiennes
<br>**$`\boldsymbol{\mathbf{\overrightarrow{rot}\,\overrightarrow{X}\,= `$
<br>**$`\boldsymbol{\mathbf{div\,\overrightarrow{X}\,=\,\color{gray}{\dfrac{d\Phi_X}{d\tau}}\,=\,\dfrac{\partial X_x}{\partial x}+\dfrac{\partial X_y}{\partial y}+\dfrac{\partial X_z}{\partial z}
}}`$**
##### Expression du rotationnel en coordonnées cylindriques
<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 du rotationnel en coordonnées sphériques
<br>**$`\boldsymbol{d\mathbf{iv\,\overrightarrow{X}\color{gray}{\;=\dfrac{d\Phi_X}{d\tau}}\,=
\; \dfrac{1}{r^2}\;\dfrac{\partial\,(r^2\,X_r}{\partial\,r)}}}`$**
**$`\hspace{4.5cm}\boldsymbol{\mathbf{+ \dfrac{1}{r\,sin\,\theta}\;\dfrac{\partial\,(sin\,\theta\,X_{\theta})}{\partial\,\theta}}}`$**
**$`\hspace{6.2cm}\boldsymbol{\mathbf{+ \dfrac{1}{r\,sin\,\theta}\;\dfrac{\partial\,X_{\varphi}}{\partial\,\varphi}}}`$**
<!--
<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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