Commit 62ec349a authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent e22c51e2
Pipeline #13705 canceled with stage
......@@ -68,10 +68,12 @@ PRINCIPALES COMBINAISONS
* <details markdown=1>
<summary>Expressions en coordonnées cylindriques et sphériques</summary>
* coordonnées cylindriques $`(\rho\,,\,\varphi\,,\,z)`$ :
<br>
$`\Delta\,\phi=\dfrac{1}{\rho}\dfrac{\partial}{\partial \rho}\left(\rho\,\dfrac{\partial \phi}{\partial \rho}\right)
+\dfrac{1}{\rho^2}\dfrac{\partial^2 \phi}{\partial \varphi^2}+\dfrac{\partial^2 \phi}{\partial z^2}`$
* coordonnées sphérique $`(r\,,\,\theta\,,\,\varphi)`$ :
$`\Delta\,\phi=\dfrac{1}{r}\dfrac{\partial^2}{\partial r^2}(r\phi}
<br>
$`\Delta\,\phi=\dfrac{1}{r}\dfrac{\partial^2}{\partial r^2}(r\phi)
+ \dfrac{1}{r^2\,\sin\theta}\dfrac{\partial}{\partial \theta}\left(\sin\theta\dfrac{\partial \phi}{\partial \theta}\right)
+ \dfrac{1}{r^2\,\sin^2\theta}\dfrac{\partial^2 \phi}{\partial \varphi^2}`$
......@@ -108,12 +110,13 @@ PRINCIPALES COMBINAISONS
* <details markdown=1>
<summary>Expressions en coordonnées cylindriques et sphériques</summary>
* dans la base cylindrique unitaire $`(\vec{e_{\rho}}\,,\,\vec{e_{\phi}}\,,\,\vec{e_z})`$ :
<br>
$`\Delta\,\overrightarrow{U}=\left(\begin{array}{l}
\dfrac{\partial^2 U_x}{\partial x^2}+\dfrac{\partial^2 U_x}{\partial x^2}+\dfrac{\partial^2 U_x}{\partial x^2}\\
\dfrac{\partial^2 U_y}{\partial x^2}+\dfrac{\partial^2 U_y}{\partial x^2}+\dfrac{\partial^2 U_y}{\partial x^2}\\
\dfrac{\partial^2 U_z}{\partial x^2}+\dfrac{\partial^2 U_z}{\partial x^2}+\dfrac{\partial^2 U_z}{\partial x^2}
\end{array}\right)`$
* dans la base sphérique unitaire $`(\vec{e_r}\,,\,\vec{e_{\theta}}\,,\,\vec{e_{\phi}})`$ :
* dans la base sphérique unitaire $`(\vec{e_r}\,,\,\vec{e_{\theta}}\,,\,\vec{e_{\phi}})`$ :
</details>
......
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