Commit 9b9e8229 authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent b3c0eaf8
Pipeline #19521 canceled with stage
...@@ -25,6 +25,9 @@ div\,\overrightarrow{X}}\;\color{black}{=\;\dfrac{d\Phi_X}{d\tau}}\; ...@@ -25,6 +25,9 @@ div\,\overrightarrow{X}}\;\color{black}{=\;\dfrac{d\Phi_X}{d\tau}}\;
<br>**$`div\,\overrightarrow{X}\;=\;\color{gray}{\dfrac{d\Phi_X}{d\tau}}\;=\;\dfrac{\partial X_x}{\partial x}+\dfrac{\partial X_y}{\partial y}+\dfrac{\partial X_z}{\partial z} <br>**$`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}
`$** `$**
<br>**$`\mathbf{div\,\overrightarrow{X}\;=\;\color{black}{\dfrac{d\Phi_X}{d\tau}}\;=\;\dfrac{\partial X_x}{\partial x}+\dfrac{\partial X_y}{\partial y}+\dfrac{\partial X_z}{\partial z}
}`$**
##### Expression de la divergence en coordonnées cylindriques ##### Expression de la divergence en coordonnées cylindriques
<br>**$`\mathbf{div\,\overrightarrow{X}}`$**$`\boldsymbol{\mathbf{\;=\dfrac{d\Phi_X}{d\tau}}}`$**$`\boldsymbol{\mathbf{\;=\dfrac{1}{\rho}\;\dfrac{\partial\,(\,\rho\,X_{\rho})}{\partial\,\rho} <br>**$`\mathbf{div\,\overrightarrow{X}}`$**$`\boldsymbol{\mathbf{\;=\dfrac{d\Phi_X}{d\tau}}}`$**$`\boldsymbol{\mathbf{\;=\dfrac{1}{\rho}\;\dfrac{\partial\,(\,\rho\,X_{\rho})}{\partial\,\rho}
...@@ -47,10 +50,10 @@ div\,\overrightarrow{X}\color{grey{\;=\;\dfrac{d\Phi_X}{d\tau}}\,=\; &\dfrac{1}{ ...@@ -47,10 +50,10 @@ div\,\overrightarrow{X}\color{grey{\;=\;\dfrac{d\Phi_X}{d\tau}}\,=\; &\dfrac{1}{
<br> <br>
**$`\mathbf{\boldsymbol{\begin{matrix} **$`\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}\\ 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 + \dfrac{1}{r\,sin\,\theta}\;\dfrac{\partial\,(sin\,\theta\,X_{\theta})}{\partial\,\theta}\\
& \quad\quad\quad\quad + \dfrac{1}{r\,sin\,\theta}\;\dfrac{\partial\,X_{\varphi}}{\partial\,\varphi}\end{matrix}}}`$** & \quad\quad\quad\quad + \dfrac{1}{r\,sin\,\theta}\;\dfrac{\partial\,X_{\varphi}}{\partial\,\varphi}\end{align}}}`$**
<br> <br>
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