Commit 04cd164c authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent 2efc19b2
Pipeline #15181 canceled with stage
...@@ -218,21 +218,21 @@ RÉSUMÉ ...@@ -218,21 +218,21 @@ RÉSUMÉ
<br> <br>
**$`\begin{align} **$`\begin{align}
\dfrac{d\overrightarrow{e_{\rho}}}{dt}&=\dfrac{d(\cos\varphi)}{dt}\,\overrightarrow{e_x}+\dfrac{d(\sin\varphi)}{dt}\,\overrightarrow{e_y}\\ \dfrac{d\overrightarrow{e_{\rho}}}{dt}&=\dfrac{d(\cos\varphi)}{dt}\,\overrightarrow{e_x}+\dfrac{d(\sin\varphi)}{dt}\,\overrightarrow{e_y}\\
&=\dots\end{align}`$** &=\dots\end{align}`$**
<br> <br>
**$`\begin{align} **$`\begin{align}
\dfrac{d\overrightarrow{e_{\varphi}}}{dt}&=\dfrac{d(-\sin\varphi)}{dt}\,\overrightarrow{e_x}+\dfrac{d(\cos\varphi)}{dt}\,\overrightarrow{e_y}\\ \dfrac{d\overrightarrow{e_{\varphi}}}{dt}&=\dfrac{d(-\sin\varphi)}{dt}\,\overrightarrow{e_x}+\dfrac{d(\cos\varphi)}{dt}\,\overrightarrow{e_y}\\
&=\dots\end{align}`$** &=\dots\end{align}`$**
<br> <br>
* en *coordonnées sphériques $`(r,\theta,\varphi)`$* * en *coordonnées sphériques $`(r,\theta,\varphi)`$*
<br> <br>
*$`\overrightarrow{e_r}(t)=+\sin\theta(t)\cos\varphi(t)\,\overrightarrow{e_x}`$* *$`\overrightarrow{e_r}(t)=+\sin\theta(t)\cos\varphi(t)\,\overrightarrow{e_x}`$*
*$`\;+\,\sin\theta(t)\sin\varphi(t),\overrightarrow{e_y}`$* *$`\;+\,\sin\theta(t)\sin\varphi(t),\overrightarrow{e_y}`$*
*$`\;+\,\cos\theta(t)\,\overrightarrow{e_z}`$* *$`\;+\,\cos\theta(t)\,\overrightarrow{e_z}`$*
<br> <br>
*$`\overrightarrow{e_{\theta}}(t)=+\cos\theta(t)\cos\varphi(t)\,\overrightarrow{e_x}`$* *$`\overrightarrow{e_{\theta}}(t)=+\cos\theta(t)\cos\varphi(t)\,\overrightarrow{e_x}`$*
*$`\;+\,\cos\theta(t)\sin\varphi(t),\overrightarrow{e_y}`$* *$`\;+\,\cos\theta(t)\sin\varphi(t),\overrightarrow{e_y}`$*
*$`\;-\,\sin\theta(t)\,\overrightarrow{e_z}`$* *$`\;-\,\sin\theta(t)\,\overrightarrow{e_z}`$*
<br> <br>
*$`\overrightarrow{e_{\varphi}}(t)=-\sin\varphi(t)\,\overrightarrow{e_x}`$* *$`\overrightarrow{e_{\varphi}}(t)=-\sin\varphi(t)\,\overrightarrow{e_x}`$*
*$`\;+\,\cos\varphi(t)\,\overrightarrow{e_y}+0\,\overrightarrow{e_z}`$* *$`\;+\,\cos\varphi(t)\,\overrightarrow{e_y}+0\,\overrightarrow{e_z}`$*
...@@ -241,15 +241,15 @@ RÉSUMÉ ...@@ -241,15 +241,15 @@ RÉSUMÉ
<br> <br>
**$`\dfrac{d\overrightarrow{e_r}}{dt}=\dfrac{d(\sin\theta\,\cos\varphi)}{dt}\,\overrightarrow{e_x}`$** **$`\dfrac{d\overrightarrow{e_r}}{dt}=\dfrac{d(\sin\theta\,\cos\varphi)}{dt}\,\overrightarrow{e_x}`$**
**$`\;+\,\dfrac{d(\sin\theta\,\sin\varphi)}{dt}\,\overrightarrow{e_y}`$** **$`\;+\,\dfrac{d(\sin\theta\,\sin\varphi)}{dt}\,\overrightarrow{e_y}`$**
**$`\;+\,\dfrac{d(\cos\theta)}{dt}\,\overrightarrow{e_z}`$** **$`\;+\,\dfrac{d(\cos\theta)}{dt}\,\overrightarrow{e_z}`$**
<br> <br>
**$`\dfrac{d\overrightarrow{e_r}}{dt}=\dfrac{d(\cos\theta\,\cos\varphi)}{dt}\,\overrightarrow{e_x}`$** **$`\dfrac{d\overrightarrow{e_r}}{dt}=\dfrac{d(\cos\theta\,\cos\varphi)}{dt}\,\overrightarrow{e_x}`$**
**$`\;+\,\dfrac{d(\cos\theta\,\sin\varphi)}{dt}\,\overrightarrow{e_y}`$** **$`\;+\,\dfrac{d(\cos\theta\,\sin\varphi)}{dt}\,\overrightarrow{e_y}`$**
**$`\;+\,\dfrac{d(-\sin\theta)}{dt}\,\overrightarrow{e_z}`$** **$`\;+\,\dfrac{d(-\sin\theta)}{dt}\,\overrightarrow{e_z}`$**
<br> <br>
**$`\dfrac{d\overrightarrow{e_r}}{dt}=\dfrac{d(-\sin\varphi)}{dt}\,\overrightarrow{e_x}`$** **$`\dfrac{d\overrightarrow{e_r}}{dt}=\dfrac{d(-\sin\varphi)}{dt}\,\overrightarrow{e_x}`$**
**$`\;+\,\dfrac{d(\cos\varphi)}{dt}\,\overrightarrow{e_y}`$** **$`\;+\,\dfrac{d(\cos\varphi)}{dt}\,\overrightarrow{e_y}`$**
**$`\;+\,0\,\overrightarrow{e_z}`$** **$`\;+\,0\,\overrightarrow{e_z}`$**
......
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