Update textbook.fr.md

12.temporary_ins/40.classical-mechanics/30.n3/07.coherence/textbook.fr.md

@@ -511,7 +511,7 @@ $`\overrightarrow{e_{\theta}}=-\sin\theta\;\overrightarrow{e_x}+\cos\theta\;\ove
 ------------------------
 
 $`\begin{align}
-\mathbf{\dfrac{d\overrightarrow{e_{\rho}}}{dt}}&=\dfrac{d}{dt}\bigg(\cos\theta\;\overrightarrow{e_x}+\sin\theta\;\overrightarrow{e_z}\bigg)\\
+\dfrac{d\overrightarrow{e_{\rho}}}{dt}&=\dfrac{d}{dt}\bigg(\cos\theta\;\overrightarrow{e_x}+\sin\theta\;\overrightarrow{e_z}\bigg)\\
 \\
 &=\bigg[\dfrac{d\cos\theta}{dt}\;\overrightarrow{e_x} + \sin\theta\;\underbrace{\dfrac{d\overrightarrow{e_z}}{dt}}_{=\,\vec{0}}\bigg]\\
 &\quad\quad+\bigg[\dfrac{d(-\sin\theta)}{dt}\;\overrightarrow{e_z}+\cos\theta\;\underbrace{\dfrac{d\overrightarrow{e_z}}{dt}}_{=\,\vec{0}}\bigg]\\
@@ -521,15 +521,15 @@ $`\begin{align}
 \\
 &=\omega\;\big(-\sin\theta\;\overrightarrow{e_x}+\cos\theta\;\overrightarrow{e_z}\big)\\
 \\
-&\mathbf{=\omega\;\overrightarrow{e_{\theta}}}
+&=\omega\;\overrightarrow{e_{\theta}}
 \end{align}`$
 
 --------------
 
 $`\begin{align}
-\mathbf{\dfrac{d\overrightarrow{e_{\theta}}}{dt}}&=\dfrac{d}{dt}\big(-\sin\theta\;\overrightarrow{e_x}+\cos\theta\;\overrightarrow{e_z}\big)\\
+\dfrac{d\overrightarrow{e_{\theta}}}{dt}&=\dfrac{d}{dt}\big(-\sin\theta\;\overrightarrow{e_x}+\cos\theta\;\overrightarrow{e_z}\big)\\
 \\
-&=\\bigg[\dfrac{d(-\sin\theta)}{dt}\;\overrightarrow{e_x} - \sin\theta\;\underbrace{\dfrac{d\overrightarrow{e_z}}{dt}}_{=\,\vec{0}}\\bigg]\\
+&=\\bigg[\dfrac{d(-\sin\theta)}{dt}\;\overrightarrow{e_x} - \sin\theta\;\underbrace{\dfrac{d\overrightarrow{e_z}}{dt}}_{=\,\vec{0}}\bigg]\\
 &\quad\quad+\bigg[\dfrac{d\cos\theta}{dt}\;\overrightarrow{e_z}+\cos\theta\;\underbrace{\dfrac{d\overrightarrow{e_z}}{dt}}_{=\,\vec{0}}\bigg]\\
 \\
 &=\dfrac{d(-\sin\theta)}{d\theta}\;\underbrace{\dfrac{d\theta}{dt}}_{=\,\omega}\;\overrightarrow{e_x}
@@ -537,13 +537,13 @@ $`\begin{align}
 \\
 &=\omega\;\Big(-\cos\theta\;\overrightarrow{e_x}-\sin\theta\;\overrightarrow{e_z}\Big)\\
 \\
-&\mathbf{=-\;\omega\;\overrightarrow{e_{\rho}}}
+&=-\;\omega\;\overrightarrow{e_{\rho}}
 \end{align}`$
 
 ---------------
 
 $`\begin{align}
-\mathbf{\dfrac{d^2\overrightarrow{e_{\rho}}}{dt^2}}&=\dfrac{d}{dt}\bigg(\underbrace{\dfrac{d\overrightarrow{e_{\rho}}}{dt}}_{=\,\omega\,\vec{e_{\theta}}}\bigg)\\
+\dfrac{d^2\overrightarrow{e_{\rho}}}{dt^2}&=\dfrac{d}{dt}\bigg(\underbrace{\dfrac{d\overrightarrow{e_{\rho}}}{dt}}_{=\,\omega\,\vec{e_{\theta}}}\bigg)\\
 \\
 &=\dfrac{d}{dt}\left(\omega\,\overrightarrow{e_{\theta}}\right)\\
 \\
@@ -551,13 +551,13 @@ $`\begin{align}
 \\
 &=\dfrac{d\omega}{dt}\;\overrightarrow{e_{\theta}}\;+\;\omega\;\big(-\,\omega\;\overrightarrow{e_{\rho}}\big)\\
 \\
-&\mathbf{=\dfrac{d\omega}{dt}\;\overrightarrow{e_{\theta}}\;-\;\omega^2\;\overrightarrow{e_{\rho}}}
+&=\dfrac{d\omega}{dt}\;\overrightarrow{e_{\theta}}\;-\;\omega^2\;\overrightarrow{e_{\rho}}
 \end{align}`$
 
 ---------------
 
 $`\begin{align}
-\mathbf{\dfrac{d^2\overrightarrow{e_{\theta}}}{dt^2}}
+\dfrac{d^2\overrightarrow{e_{\theta}}}{dt^2}
 &=\dfrac{d}{dt}\bigg(\underbrace{\dfrac{d\overrightarrow{e_{\theta}}}{dt}}_{=-\omega\,\vec{e_{\rho}}}\bigg)\\
 \\
 &=\dfrac{d}{dt}\left(-\omega\,\overrightarrow{e_{\rho}}\right)\\
@@ -566,7 +566,7 @@ $`\begin{align}
 \\
 &=-\dfrac{d\omega}{dt}\;\overrightarrow{e_{\rho}}\;-\;\omega\;\big(\omega\;\overrightarrow{e_{\theta}}\big)\\
 \\
-&\mathbf{=\dfrac{d\omega}{dt}\;\overrightarrow{e_{\rho}}\;-\;\omega^2\;\overrightarrow{e_{\theta}}}
+&=\dfrac{d\omega}{dt}\;\overrightarrow{e_{\rho}}\;-\;\omega^2\;\overrightarrow{e_{\theta}}
 \end{align}`$