Update textbook.fr.md

12.temporary_ins/40.classical-mechanics/30.n3/42.point-dynamics-applications/05.point-dynamics-method/10.main/textbook.fr.md

@@ -106,15 +106,16 @@ $`\displaystyle\quad\; =\dpt{\overrightarrow{OO'}}
 +\sum_{i=1}^3 \Big(\dpt{\alpha_{iM}}\cdot\overrightarrow{e_{\alpha_{i}}}_M+\alpha_{iM}\cdot\dpt{\overrightarrow{e_{\alpha_{i}}}}_M\Big)`$
 <br>
 $`\displaystyle\quad\; =\dpt{\overrightarrow{OO'}}
-+\sum_{i=1}^3 \dpt{\alpha_{iM}}\cdot\overrightarrow{e_{\alpha_{i}}}_M\;+\;\sum_{i=1}^3\alpha_{iM}\cdot\dpt{\overrightarrow{e_{\alpha_{i}}}}_M`$
++\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 $`\overrightarrow{a_M}`$  
 <br>
-$`\overrightarrow{a_M}=\dpt{\overrightarrow{v_M}}=\ddpt{\overrightarrow{OM}}}=\ddpt{\overrightarrow{OO'}}+\ddpt{\overrightarrow{O'M}}`$   
+$`\overrightarrow{a_M}=\dpt{\overrightarrow{v_M}}=\ddpt{\overrightarrow{OM}}`$   
 <br>
-$`\quad\quad=\ddpt{\overrightarrow{OO'}}+\dpt{\overrightarrow{v_M}}`$ 
-<br>
-$`\quad\quad =\dpt{\overrightarrow{OO'}}
-+\dpt{\alpha_{1\;M}}\,\overrightarrow{e_{\alpha_{1}}}_M+\alpha_{1\;M}\,\dpt{\overrightarrow{e_{\alpha_{1}}}}_M
-+\dpt{\alpha_{2\;M}}\,\overrightarrow{e_{\alpha_{2}}}_M+\alpha_{2\;M}\,\dpt{\overrightarrow{e_{\alpha_{2}}}}_M
-+\dpt{\alpha_{3\;M}}\,\overrightarrow{e_{\alpha_{3}}}_M+\alpha_{3\;M}\,\dpt{\overrightarrow{e_{\alpha_{3}}}}_M`$ 
+$`\displaystyle\quad\quad =\ddpt{\overrightarrow{OO'}}
++\Big(\sum_{i=1}^3 \ddpt{\alpha_{iM}}\cdot\overrightarrow{e_{\alpha_{i}}}_M + \dpt{\alpha_{iM}}\cdot\dpt{\overrightarrow{e_{\alpha_{i}}}}_M
+\Big)
++
+\Big(
+\sum_{i=1}^3 \dpt{\alpha_{iM}}\cdot\dpt{\overrightarrow{e_{\alpha_{i}}}}_M + \alpha_{iM}\cdot\ddpt{\overrightarrow{e_{\alpha_{i}}}}_M
+\Big)`$