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 ...@@ -68,10 +68,12 @@ PRINCIPALES COMBINAISONS
* <details markdown=1> * <details markdown=1>
<summary>Expressions en coordonnées cylindriques et sphériques</summary> <summary>Expressions en coordonnées cylindriques et sphériques</summary>
* coordonnées cylindriques $`(\rho\,,\,\varphi\,,\,z)`$ : * coordonnées cylindriques $`(\rho\,,\,\varphi\,,\,z)`$ :
<br>
$`\Delta\,\phi=\dfrac{1}{\rho}\dfrac{\partial}{\partial \rho}\left(\rho\,\dfrac{\partial \phi}{\partial \rho}\right) $`\Delta\,\phi=\dfrac{1}{\rho}\dfrac{\partial}{\partial \rho}\left(\rho\,\dfrac{\partial \phi}{\partial \rho}\right)
+\dfrac{1}{\rho^2}\dfrac{\partial^2 \phi}{\partial \varphi^2}+\dfrac{\partial^2 \phi}{\partial z^2}`$ +\dfrac{1}{\rho^2}\dfrac{\partial^2 \phi}{\partial \varphi^2}+\dfrac{\partial^2 \phi}{\partial z^2}`$
* coordonnées sphérique $`(r\,,\,\theta\,,\,\varphi)`$ : * coordonnées sphérique $`(r\,,\,\theta\,,\,\varphi)`$ :
$`\Delta\,\phi=\dfrac{1}{r}\dfrac{\partial^2}{\partial r^2}(r\phi} <br>
$`\Delta\,\phi=\dfrac{1}{r}\dfrac{\partial^2}{\partial r^2}(r\phi)
+ \dfrac{1}{r^2\,\sin\theta}\dfrac{\partial}{\partial \theta}\left(\sin\theta\dfrac{\partial \phi}{\partial \theta}\right) + \dfrac{1}{r^2\,\sin\theta}\dfrac{\partial}{\partial \theta}\left(\sin\theta\dfrac{\partial \phi}{\partial \theta}\right)
+ \dfrac{1}{r^2\,\sin^2\theta}\dfrac{\partial^2 \phi}{\partial \varphi^2}`$ + \dfrac{1}{r^2\,\sin^2\theta}\dfrac{\partial^2 \phi}{\partial \varphi^2}`$
...@@ -108,6 +110,7 @@ PRINCIPALES COMBINAISONS ...@@ -108,6 +110,7 @@ PRINCIPALES COMBINAISONS
* <details markdown=1> * <details markdown=1>
<summary>Expressions en coordonnées cylindriques et sphériques</summary> <summary>Expressions en coordonnées cylindriques et sphériques</summary>
* dans la base cylindrique unitaire $`(\vec{e_{\rho}}\,,\,\vec{e_{\phi}}\,,\,\vec{e_z})`$ : * dans la base cylindrique unitaire $`(\vec{e_{\rho}}\,,\,\vec{e_{\phi}}\,,\,\vec{e_z})`$ :
<br>
$`\Delta\,\overrightarrow{U}=\left(\begin{array}{l} $`\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_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_y}{\partial x^2}+\dfrac{\partial^2 U_y}{\partial x^2}+\dfrac{\partial^2 U_y}{\partial x^2}\\
......
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