Update textbook.fr.md

12.temporary_ins/40.classical-mechanics/40.n4/70.lagrangian-mechanics/07.coherence/textbook.fr.md

@@ -174,15 +174,15 @@ $`\displaystyle\;=\int_{\alpha_1}^{\alpha_2}\dfrac{d (uv)}{d\alpha}\,d\alpha
 $`\dfrac{\partial\mathcal{L}}{\partial \dpt{x}_i} \cdot\delta \dpt{x}_i`$
 $`\;=\dfrac{\partial\mathcal{L}}{\partial \dpt{x}_i}\cdot\dfrac{d\,\delta x_i}{dt}`$
 
-$`u=\dfrac{\partial \mathcal{L}}{\partial\dpt{x}}`$
+$`u_i=\dfrac{\partial \mathcal{L}}{\partial\dpt{x_i}}`$
 
-$`\dfrac{du}{dt}=\dfrac{d}{dt}\bigg(\,\dfrac{\partial \mathcal{L}}{\partial\dpt{x}}\bigg)`$
+$`\dfrac{du_i}{dt}=\dfrac{d}{dt}\bigg(\,\dfrac{\partial \mathcal{L}}{\partial\dpt{x}_i}\bigg)`$
 
-$`v=\delta x`$
-
-$`\dfrac{dv}{dt}=\dfrac{d\,\delta x}{dt}`$
+$`v_i=\delta x_i`$
 
+$`\dfrac{dv_i}{dt}=\dfrac{d\,\delta x_i}{dt}`$
 
+$`\dfrac{\partial\mathcal{L}}{\partial \dpt{x}_i} \cdot\delta \dpt{x}_i`$
 $`\quad=\dfrac{d}{dt}\bigg(\,\dfrac{\partial\mathcal{L}}{\partial \dpt{x}_i}\cdot \delta x_i\bigg)
 -\dfrac{d}{dt}\bigg(\,\dfrac{\partial\mathcal{L}}{\partial \dpt{x}_i}\bigg)\cdot \delta x_i`$