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Commit c7efce1d authored by Claude Meny's avatar Claude Meny
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Update textbook.fr.md

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    12.temporary_ins/40.classical-mechanics/40.n4/70.lagrangian-mechanics/07.coherence/textbook.fr.md
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    ...@@ -223,16 +223,18 @@ $`\delta \mathcal{S}=\displaystyle\int_{t_1}^{t_2} ...@@ -223,16 +223,18 @@ $`\delta \mathcal{S}=\displaystyle\int_{t_1}^{t_2}
    $`\quad=\displaystyle\int_{t_1}^{t_2} $`\quad=\displaystyle\int_{t_1}^{t_2}
    \bigg[ \bigg[
    \dfrac{\partial\mathcal{L}}{\partial x_i}\cdot \delta x_i \dfrac{\partial\mathcal{L}}{\partial x_i}
    -\dfrac{d}{dt}\dfrac{\partial\mathcal{L}}{\partial \dpt{x}_i}\bigg]\,\delta x_i\,dt`$ -\dfrac{d}{dt}\dfrac{\partial\mathcal{L}}{\partial \dpt{x}_i}\bigg]\,\delta x_i\,dt`$
    Stationnarité de l'action impose $`\delta \mathcal{S}=0`$ Stationnarité de l'action impose $`\delta \mathcal{S}=0`$
    d'où l'équation d'Euler-Lagrange : d'où l'équation d'Euler-Lagrange :
    $`\dfrac{\partial\mathcal{L}}{\partial x_i}\cdot \delta x_i $`\dfrac{\partial\mathcal{L}}{\partial x_i}
    -\dfrac{d}{dt}\dfrac{\partial\mathcal{L}}{\partial \dpt{x}_i}`$ -\dfrac{d}{dt}\dfrac{\partial\mathcal{L}}{\partial \dpt{x}_i}=0`$
    $`\dfrac{\partial\mathcal{L}}{\partial x_i}
    -\dfrac{d}{dt}\bigg(\,\dfrac{\partial\mathcal{L}}{\partial \dpt{x}_i}\bigg)=0`$
    ......
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