Commit 30bc6e0e authored by Claude Meny's avatar Claude Meny

Update textbook.fr.md

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...@@ -90,39 +90,39 @@ pour conduire l'étude. ...@@ -90,39 +90,39 @@ pour conduire l'étude.
Ecriture générale de la position d'un point $`M`$ quelconque : Ecriture générale de la position d'un point $`M`$ quelconque :
<br> <br>
$`\overrightarrow{OM}=\overrightarrow{OO'}+\overrightarrow{O'M}`$ **$`\mathbf{\overrightarrow{OM}}`$** $`\;=\overrightarrow{OO'}+\overrightarrow{O'M}`$
<br> <br>
$`\hspace{1.0cm} =\overrightarrow{OO'}+\alpha_{1M}\cdot\overrightarrow{e_{\alpha_{1}}}_M $`\hspace{1.0cm} =\overrightarrow{OO'}+\alpha_{1M}\cdot\overrightarrow{e_{\alpha_{1}}}_M
+\alpha_{2M}\cdot\overrightarrow{e_{\alpha_{2}}}_M +\alpha_{2M}\cdot\overrightarrow{e_{\alpha_{2}}}_M
+\alpha_{3M}\cdot\overrightarrow{e_{\alpha_{3}}}_M `$ +\alpha_{3M}\cdot\overrightarrow{e_{\alpha_{3}}}_M `$
<br> <br>
$`\displaystyle\quad\;\, =\overrightarrow{OO'}+\sum_{i=1}^3 \alpha_{iM}\cdot\overrightarrow{e_{\alpha_{i}}}_M`$ **$`\displaystyle\hspace{1.0cm} \mathbf{=\overrightarrow{OO'}+\sum_{i=1}^3 \alpha_{iM}\cdot\overrightarrow{e_{\alpha_{i}}}_M}`$**
Ecriture générale de son vecteur vitesse $`\overrightarrow{v_M}`$ Ecriture générale de son vecteur vitesse $`\overrightarrow{v_M}`$
<br> <br>
**$`\overrightarrow{v_M}`$** **$`\mathbf{\overrightarrow{v_M}}`$**
*$`\;=\dpt{\overrightarrow{OM}}`$* $`\;=\dpt{\overrightarrow{OO'}}+\dpt{\overrightarrow{O'M}}`$ *$`\mathbf{\;=\dpt{\overrightarrow{OM}}}`$* $`\;=\dpt{\overrightarrow{OO'}}+\dpt{\overrightarrow{O'M}}`$
<br> <br>
$`\displaystyle\hspace{1.0cm}=\dpt{\overrightarrow{OO'}} $`\displaystyle\hspace{1.0cm}=\dpt{\overrightarrow{OO'}}
+\sum_{i=1}^3 \Big(\dpt{\alpha_{iM}}\cdot\overrightarrow{e_{\alpha_{i}}}_M+\alpha_{iM}\cdot\dpt{\overrightarrow{e_{\alpha_{i}}}}_M\Big)`$ +\sum_{i=1}^3 \Big(\dpt{\alpha_{iM}}\cdot\overrightarrow{e_{\alpha_{i}}}_M+\alpha_{iM}\cdot\dpt{\overrightarrow{e_{\alpha_{i}}}}_M\Big)`$
<br> <br>
$`\displaystyle\hspace{1.0cm}=\dpt{\overrightarrow{OO'}} **$`\displaystyle\hspace{1.0cm}\mathbf{=\dpt{\overrightarrow{OO'}}
+\sum_{i=1}^3 \dpt{\alpha_{iM}}\cdot\overrightarrow{e_{\alpha_{i}}}_M + \sum_{i=1}^3\alpha_{iM}\cdot\dpt{\overrightarrow{e_{\alpha_{i}}}}_M`$ +\sum_{i=1}^3 \dpt{\alpha_{iM}}\cdot\overrightarrow{e_{\alpha_{i}}}_M + \sum_{i=1}^3\alpha_{iM}\cdot\dpt{\overrightarrow{e_{\alpha_{i}}}}_M}`$**
Ecriture générale de son vecteur accélération $`\overrightarrow{a_M}`$ Ecriture générale de son vecteur accélération $`\overrightarrow{a_M}`$
<br> <br>
**$`\overrightarrow{a_M}`$** **$`\mathbf{\overrightarrow{a_M}}`$**
*$`\;=\dpt{\overrightarrow{v_M}}=\ddpt{\overrightarrow{OM}}`$* *$`\mathbf{\;=\dpt{\overrightarrow{v_M}}=\ddpt{\overrightarrow{OM}}}`$*
<br> <br>
$`\displaystyle\begin{align}\hspace{1.0cm} =\ddpt{\overrightarrow{OO'}} $`\displaystyle\begin{align}\hspace{1.0cm} =\ddpt{\overrightarrow{OO'}}
& +\sum_{i=1}^3 \Big(\ddpt{\alpha_{iM}}\cdot\overrightarrow{e_{\alpha_{i}}}_M + \dpt{\alpha_{iM}}\cdot\dpt{\overrightarrow{e_{\alpha_{i}}}}_M\Big) \\ & +\sum_{i=1}^3 \Big(\ddpt{\alpha_{iM}}\cdot\overrightarrow{e_{\alpha_{i}}}_M + \dpt{\alpha_{iM}}\cdot\dpt{\overrightarrow{e_{\alpha_{i}}}}_M\Big) \\
& +\sum_{i=1}^3 \Big(\dpt{\alpha_{iM}}\cdot\dpt{\overrightarrow{e_{\alpha_{i}}}}_M + \alpha_{iM}\cdot\ddpt{\overrightarrow{e_{\alpha_{i}}}}_M\Big) & +\sum_{i=1}^3 \Big(\dpt{\alpha_{iM}}\cdot\dpt{\overrightarrow{e_{\alpha_{i}}}}_M + \alpha_{iM}\cdot\ddpt{\overrightarrow{e_{\alpha_{i}}}}_M\Big)
\end{align}`$ \end{align}`$
<br> <br>
**$`\displaystyle\begin{align}\hspace{1.0cm} =\ddpt{\overrightarrow{OO'}} **$`\displaystyle\begin{align}\hspace{1.0cm} \mathbf{=\ddpt{\overrightarrow{OO'}}
& +\sum_{i=1}^3 \ddpt{\alpha_{iM}}\cdot\overrightarrow{e_{\alpha_{i}}}_M \\ & +\sum_{i=1}^3 \ddpt{\alpha_{iM}}\cdot\overrightarrow{e_{\alpha_{i}}}_M \\
& + \Big( 2\times \sum_{i=1}^3 \dpt{\alpha_{iM}}\cdot\dpt{\overrightarrow{e_{\alpha_{i}}}}_M \Big) \\ & + \Big( 2\times \sum_{i=1}^3 \dpt{\alpha_{iM}}\cdot\dpt{\overrightarrow{e_{\alpha_{i}}}}_M \Big) \\
& + \sum_{i=1}^3 \alpha_{iM}\cdot\ddpt{\overrightarrow{e_{\alpha_{i}}}}_M & + \sum_{i=1}^3 \alpha_{iM}\cdot\ddpt{\overrightarrow{e_{\alpha_{i}}}}_M}
\end{align}`$** \end{align}`$**
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