mise a jour du rapport
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latex/Illustrations/Q40100.png
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latex/Illustrations/Q40200.png
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latex/Illustrations/Q40400.png
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latex/Illustrations/Q4eigenValTEMPSCONT.png
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latex/Illustrations/Q4eigenValTEMPSCONT.png
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latex/Illustrations/Q5stepReponse.png
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40
latex/Questions/Q1.tex
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40
latex/Questions/Q1.tex
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@ -0,0 +1,40 @@
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\textbf{Question 1}
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En considérant le modèle EDP suivant ainsi que les équations données pour $e_1$ et $e_2$ :
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\begin{equation}
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\rho(\zeta)\frac{\partial^2 \omega}{\partial t^2}
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=
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-\frac{\partial^2}{\partial \zeta^2}
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\left(
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EI(\zeta)\frac{\partial^2 \omega}{\partial \zeta^2}(\zeta,t)
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\right)
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-q(\zeta,t)
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\end{equation}
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On obtient comme la représentation d'état :
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\begin{equation}
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\dot{x}
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=
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\begin{bmatrix}
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\dot{x}_1 \\
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\dot{x}_2
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\end{bmatrix}
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=
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\frac{\partial^2}{\partial \zeta^2}
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\begin{bmatrix}
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0 & 1 \\
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-1 & 0
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\end{bmatrix}
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\begin{bmatrix}
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e_1(\zeta,t) \\
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e_2(\zeta,t)
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\end{bmatrix}
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+
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\begin{bmatrix}
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0 \\
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-q(\zeta,t)
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\end{bmatrix}
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\end{equation}
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68
latex/Questions/Q2.tex
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68
latex/Questions/Q2.tex
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@ -0,0 +1,68 @@
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\textbf{Question 2}
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À partir des informations données dans l'exercice, on peut écrire :
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\begin{equation}
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\dot{x}_1
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=
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\frac{\partial^2 e_2}{\partial \zeta^2}
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=
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\phi(\zeta)^T \dot{x}_{1d}(t)
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\end{equation}
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En multipliant les deux membres par le vecteur d'approximation $\phi(\zeta)$, on obtient :
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\begin{equation}
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\phi(\zeta)
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\frac{\partial^2 e_2}{\partial \zeta^2}
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=
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\phi(\zeta)\phi(\zeta)^T \dot{x}_{1d}(t)
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\end{equation}
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En remplaçant ensuite $e_2$ par son approximation, on obtient :
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\begin{equation}
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\phi(\zeta)
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\frac{\partial^2}{\partial \zeta^2}
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\left(
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\phi(\zeta)^T e_{2d}(t)
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\right)
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=
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\phi(\zeta)\phi(\zeta)^T \dot{x}_{1d}(t)
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\end{equation}
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Comme $e_{2d}(t)$ ne dépend pas de $\zeta$, il peut être sorti de l'intégrale. En intégrant sur $[0,L]$, on obtient :
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\begin{equation}
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\int_0^L
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\phi(\zeta)\phi(\zeta)^T
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\, d\zeta \,
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\dot{x}_{1d}(t)
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=
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\int_0^L
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\phi(\zeta)
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\frac{\partial^2 \phi(\zeta)^T}{\partial \zeta^2}
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\, d\zeta \,
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e_{2d}(t)
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\end{equation}
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On identifie alors les matrices $E$ et $D$. Ainsi, les deux équations d'état discrétisées s'écrivent :
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\begin{equation}
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\begin{aligned}
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E\dot{x}_{1d}(t) &= D e_{2d}(t),\\
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E\dot{x}_{2d}(t) &= -D^T e_{1d}(t)-\phi(L)u(t)-F_{ext}.
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\end{aligned}
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\end{equation}
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Enfin, on obtient :
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\begin{equation}
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\boxed{
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\begin{aligned}
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E\dot{x}_{1d}(t) &= D e_{2d}(t),\\
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E\dot{x}_{2d}(t) &= -D^T e_{1d}(t)-\phi(L)u(t)-F_{ext},\\
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y(t) &= -\phi(L)^T e_{2d}(t).
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\end{aligned}
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}
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\end{equation}
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65
latex/Questions/Q3.tex
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65
latex/Questions/Q3.tex
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@ -0,0 +1,65 @@
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\textbf{Question 3}
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Le système devient avec $\rho = EI = 1$ et $q(\zeta,t)=0$ :
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\begin{equation}
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\begin{aligned}
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E\dot{x}_{1d}(t) &= D x_{2d}(t),\\
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E\dot{x}_{2d}(t) &= -D^T x_{1d}(t)-\phi(L)u(t),\\
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y(t) &= -\phi(L)^T x_{2d}(t).
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\end{aligned}
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\end{equation}
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En multipliant les deux premières équations par $E^{-1}$, on obtient :
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\begin{equation}
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\begin{aligned}
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\dot{x}_{1d}(t) &= E^{-1}D x_{2d}(t),\\
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\dot{x}_{2d}(t) &= -E^{-1}D^T x_{1d}(t)-E^{-1}\phi(L)u(t).
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\end{aligned}
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\end{equation}
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En multipliant les deux premières équations par $E^{-1}$, on obtient comme valeurs de $A$, $B$ et $C$ :
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\begin{equation}
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A =
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\begin{bmatrix}
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0 & 0 & 0 & 0 & 114 & 6 & 12 & -2 \\
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0 & 0 & 0 & 0 & -54 & -6 & -2 & 4 \\
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0 & 0 & 0 & 0 & -1188 & -12 & -114 & 6 \\
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0 & 0 & 0 & 0 & -828 & -12 & -54 & 6 \\
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6 & 54 & 4 & -2 & 0 & 0 & 0 & 0 \\
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-6 & -114 & -2 & 12 & 0 & 0 & 0 & 0 \\
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-12 & -828 & -6 & 54 & 0 & 0 & 0 & 0 \\
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-12 & -1188 & -6 & 114 & 0 & 0 & 0 & 0
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\end{bmatrix}
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\end{equation}
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\begin{equation}
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B=
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\begin{bmatrix}
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0\\
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0\\
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0\\
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0\\
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4\\
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-16\\
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-60\\
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-120
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\end{bmatrix}
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\qquad
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C=
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\begin{bmatrix}
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0 & 0 & 0 & 0 & 0 & -1 & 0 & 0
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\end{bmatrix}
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\end{equation}
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Finalement,
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\begin{equation}
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\boxed{
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\begin{aligned}
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\dot{x}_d(t) &= Ax_d(t)+Bu(t),\\
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y(t) &= Cx_d(t).
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\end{aligned}
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}
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\end{equation}
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39
latex/Questions/Q4.tex
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39
latex/Questions/Q4.tex
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@ -0,0 +1,39 @@
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\textbf{Question 4}
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La Figure 1a correspond aux valeurs propres en temps continu, tandis que les figures 1b, 1c et 1d montrent les valeurs propres discrètes obtenues avec les méthodes de Tustin et ZOH pour différents temps d'échantillonnage.
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En temps continu, le système présente deux pôles à partie réelle positive, ce qui montre son instabilité.
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Après discrétisation, les pôles obtenus avec les méthodes de Tustin et ZOH se trouvent sur ou proches du cercle unité. Le système discret est donc à la limite de stabilité.
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\begin{figure}[h]
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\centering
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\begin{subfigure}{0.48\textwidth}
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\centering
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\includegraphics[width=\textwidth]{Illustrations/Q4eigenValTEMPSCONT}
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\caption{Valeurs propres en temps continu.}
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\end{subfigure}
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\hfill
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\begin{subfigure}{0.48\textwidth}
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\centering
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\includegraphics[width=\textwidth]{Illustrations/Q40100}
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\caption{$T_s = 0{,}01\,\mathrm{s}$.}
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\end{subfigure}
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\vspace{0.3cm}
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\begin{subfigure}{0.48\textwidth}
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\centering
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\includegraphics[width=\textwidth]{Illustrations/Q40200}
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\caption{$T_s = 0{,}02\,\mathrm{s}$.}
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\end{subfigure}
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\hfill
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\begin{subfigure}{0.48\textwidth}
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\centering
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\includegraphics[width=\textwidth]{Illustrations/Q40400}
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\caption{$T_s = 0{,}04\,\mathrm{s}$.}
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\end{subfigure}
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\caption{Comparaison des valeurs propres du système en temps continu et en temps discret.}
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\end{figure}
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9
latex/Questions/Q5.tex
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9
latex/Questions/Q5.tex
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@ -0,0 +1,9 @@
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\textbf{Question 5}
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La Figure 2 montre que la sortie $y(t)$ oscille après l’échelon, confirmant l’instabilité du système en boucle ouverte.
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\begin{figure}[H]
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\centering
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\includegraphics[width=0.4\textwidth]{Illustrations/Q5stepReponse} % Remplacez par votre image
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\caption{Response du système en boucle ouverte.}
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\end{figure}
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0
latex/Questions/Q6
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0
latex/Questions/Q6
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@ -2,94 +2,51 @@
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Une introduction
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\newpage
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\section{Dynamique du système avec équations differentielles partielles}
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\section{Dynamique du système avec équations différentielles partielles}
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\subsection{Espace d'état}
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\textbf{Question 1}
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L'espace d'état se trouve sous la forme:
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\begin{center}
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\begin{equation}
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\rho(\zeta)\frac{\partial^2 w}{\partial t^2}(\zeta,t) = -\frac{\partial^2}{\partial \zeta ^2}\begin{bmatrix}
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EI(\zeta )\frac{\partial^2}{\partial \zeta^2}(\zeta,t)
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\end{bmatrix}
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-q(\zeta,t)
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\end{equation}
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$E =$
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\[
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\begin{bmatrix}
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13/35 & 9/70 & 11/210 &-13/420 \\
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9/70 & 13/35 & 13/420 & -11/210\\
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11/210 & 13/420 & 1/105 & -1/140\\
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-13/420 & -11/210 & -1/140 & 1/105
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\end{bmatrix}
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\]
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\begin{equation}
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x_1(\zeta,t)=\frac{\partial^2 w}{\partial \zeta ^2}(\zeta,t) \;
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x_2(\zeta,t)=\rho(\zeta)\frac{\partial w}{\partial t}(\zeta,t)
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\end{equation}
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%%%Q1
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\input{Questions/Q1}
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%%%
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\begin{equation}
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e_1(\zeta,t)=EI(\zeta)x_1(\zeta,t) \;
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e_2(\zeta,t)=\frac{1}{\rho(\zeta)}x_2(\zeta,t)
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\end{equation}
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\begin{equation}
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\dot{x}(t)=\begin{bmatrix}
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\dot{x}_1 \\
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\dot{x}_2
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\end{bmatrix}
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= \frac{\partial^2}{\partial z^2}
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\begin{bmatrix}
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0 & 1 \\
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-1 & 0
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\end{bmatrix}
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\begin{bmatrix}
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e_1(\zeta,t) & e_2(\zeta ,t)
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\end{bmatrix}
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+
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\begin{bmatrix}
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0 \\
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-q(\zeta,t)
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\end{bmatrix}
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\end{equation}
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\end{center}
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Voici la represntation d'état à partir des equations diferentielles.
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\textbf{Question 2}
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Comment ajouter un image:
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\includegraphics[scale=1]{./Illustrations/im1.png}
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Les Poles du système avec retour d'état.
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\section{Une autre section}
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\begin{figure}[h]
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\centering
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\includegraphics[width=0.5\textwidth]{example-image} % Remplacez par votre image
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\caption{Ceci est un exemple de figure.}
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\label{fig:example}
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\end{figure}
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\begin{table}[h]
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\centering
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\caption{Ceci est un exemple de tableau.}
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\begin{tabular}{|c|c|c|}
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\hline
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Colonne 1 & Colonne 2 & Colonne 3 \\ \hline
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Donnée 1 & Donnée 2 & Donnée 3 \\ \hline
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Donnée 4 & Donnée 5 & Donnée 6 \\ \hline
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\end{tabular}
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\label{tab:example}
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\end{table}
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\section{Another section}
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\subsection{Une sous section}
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\subsubsection{Une sous sous section}
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Un mot compliqué\footnote{Une note de bas de page}
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\subsection{Discrétisation par éléments finis}
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%%Q2
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\input{Questions/Q2}
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%%%%
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>>>>>>> 10ca19c (mise a jour du rapport)
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%%Q3
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\input{Questions/Q3}
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%%
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%%Q4
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\input{Questions/Q4}
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%%
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%%%Q5
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\newpage
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\psection{Conclusion}
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Une conclusion
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\input{Questions/Q5}
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%%
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% \section{Une autre section}
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% \begin{table}[h]
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% \centering
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% \caption{Ceci est un exemple de tableau.}
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% \begin{tabular}{|c|c|c|}
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% \hline
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% Colonne 1 & Colonne 2 & Colonne 3 \\ \hline
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% Donnée 1 & Donnée 2 & Donnée 3 \\ \hline
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% Donnée 4 & Donnée 5 & Donnée 6 \\ \hline
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% \end{tabular}
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% \label{tab:example}
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% \end{table}
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% \section{Another section}
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% \subsection{Une sous section}
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% \subsubsection{Une sous sous section}
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% Un mot compliqué\footnote{Une note de bas de page}
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% \newpage
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% \psection{Conclusion}
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% Une conclusion
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\providecommand\hyper@newdestlabel[2]{}
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\providecommand\HyField@AuxAddToFields[1]{}
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\providecommand\HyField@AuxAddToCoFields[2]{}
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\providecommand\babel@aux[2]{}
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\providecommand \babel@aux [2]{\global \let \babel@toc \@gobbletwo }
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\@nameuse{bbl@beforestart}
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\catcode `:\active
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\catcode `;\active
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\catcode `!\active
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\catcode `?\active
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\abx@aux@refcontext{nty/global//global/global}
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\abx@aux@refcontext{nty/global//global/global/global}
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@ -1,5 +1,5 @@
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% $ biblatex auxiliary file $
|
||||
% $ biblatex bbl format version 3.2 $
|
||||
% $ biblatex bbl format version 3.3 $
|
||||
% Do not modify the above lines!
|
||||
%
|
||||
% This is an auxiliary file used by the 'biblatex' package.
|
||||
|
|
|
|||
20
latex/main.bbl-SAVE-ERROR
Normal file
20
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Normal file
|
|
@ -0,0 +1,20 @@
|
|||
% $ biblatex auxiliary file $
|
||||
% $ biblatex bbl format version 3.3 $
|
||||
% Do not modify the above lines!
|
||||
%
|
||||
% This is an auxiliary file used by the 'biblatex' package.
|
||||
% This file may safely be deleted. It will be recreated by
|
||||
% biber as required.
|
||||
%
|
||||
\begingroup
|
||||
\makeatletter
|
||||
\@ifundefined{ver@biblatex.sty}
|
||||
{\@latex@error
|
||||
{Missing 'biblatex' package}
|
||||
{The bibliography requires the 'biblatex' package.}
|
||||
\aftergroup\endinput}
|
||||
{}
|
||||
\endgroup
|
||||
|
||||
\endinput
|
||||
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||||
|
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@ -1,5 +1,5 @@
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|||
<?xml version="1.0" encoding="UTF-8"?>
|
||||
<bcf:controlfile version="3.10" bltxversion="3.19" xmlns:bcf="https://sourceforge.net/projects/biblatex">
|
||||
<bcf:controlfile version="3.11" bltxversion="3.21" xmlns:bcf="https://sourceforge.net/projects/biblatex">
|
||||
<!-- BIBER OPTIONS -->
|
||||
<bcf:options component="biber" type="global">
|
||||
<bcf:option type="singlevalued">
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@ -502,6 +502,7 @@
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|||
<bcf:option datatype="xml">inheritance</bcf:option>
|
||||
<bcf:option datatype="xml">translit</bcf:option>
|
||||
<bcf:option datatype="xml">uniquenametemplate</bcf:option>
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<bcf:option datatype="xml">namehashtemplate</bcf:option>
|
||||
<bcf:option datatype="xml">sortingnamekeytemplate</bcf:option>
|
||||
<bcf:option datatype="xml">sortingtemplate</bcf:option>
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||||
<bcf:option datatype="xml">extradatespec</bcf:option>
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@ -513,6 +514,7 @@
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<bcf:option datatype="string">alphaothers</bcf:option>
|
||||
<bcf:option datatype="string">sortalphaothers</bcf:option>
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<bcf:option datatype="string">presort</bcf:option>
|
||||
<bcf:option datatype="string">citepagerange</bcf:option>
|
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<bcf:option datatype="string">texencoding</bcf:option>
|
||||
<bcf:option datatype="string">bibencoding</bcf:option>
|
||||
<bcf:option datatype="string">sortingtemplatename</bcf:option>
|
||||
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@ -748,9 +750,10 @@
|
|||
</bcf:optionscope>
|
||||
<bcf:optionscope type="ENTRY">
|
||||
<bcf:option datatype="string">noinherit</bcf:option>
|
||||
<bcf:option datatype="string" backendin="sortingnamekeytemplatename,uniquenametemplatename,labelalphanametemplatename">nametemplates</bcf:option>
|
||||
<bcf:option datatype="string" backendin="sortingnamekeytemplatename,uniquenametemplatename,labelalphanametemplatename,namehashtemplatename">nametemplates</bcf:option>
|
||||
<bcf:option datatype="string" backendout="1">labelalphanametemplatename</bcf:option>
|
||||
<bcf:option datatype="string" backendout="1">uniquenametemplatename</bcf:option>
|
||||
<bcf:option datatype="string" backendout="1">namehashtemplatename</bcf:option>
|
||||
<bcf:option datatype="string" backendout="1">sortingnamekeytemplatename</bcf:option>
|
||||
<bcf:option datatype="string">presort</bcf:option>
|
||||
<bcf:option datatype="string" backendout="1">indexing</bcf:option>
|
||||
|
|
@ -827,9 +830,10 @@
|
|||
<bcf:option datatype="integer" backendout="1">minalphanames</bcf:option>
|
||||
</bcf:optionscope>
|
||||
<bcf:optionscope type="NAMELIST">
|
||||
<bcf:option datatype="string" backendin="sortingnamekeytemplatename,uniquenametemplatename,labelalphanametemplatename">nametemplates</bcf:option>
|
||||
<bcf:option datatype="string" backendin="sortingnamekeytemplatename,uniquenametemplatename,labelalphanametemplatename,namehashtemplatename">nametemplates</bcf:option>
|
||||
<bcf:option datatype="string" backendout="1">labelalphanametemplatename</bcf:option>
|
||||
<bcf:option datatype="string" backendout="1">uniquenametemplatename</bcf:option>
|
||||
<bcf:option datatype="string" backendout="1">namehashtemplatename</bcf:option>
|
||||
<bcf:option datatype="string" backendout="1">sortingnamekeytemplatename</bcf:option>
|
||||
<bcf:option datatype="string">uniquelist</bcf:option>
|
||||
<bcf:option datatype="string">uniquename</bcf:option>
|
||||
|
|
@ -843,9 +847,10 @@
|
|||
<bcf:option datatype="boolean" backendout="1">useprefix</bcf:option>
|
||||
</bcf:optionscope>
|
||||
<bcf:optionscope type="NAME">
|
||||
<bcf:option datatype="string" backendin="sortingnamekeytemplatename,uniquenametemplatename,labelalphanametemplatename">nametemplates</bcf:option>
|
||||
<bcf:option datatype="string" backendin="sortingnamekeytemplatename,uniquenametemplatename,labelalphanametemplatename,namehashtemplatename">nametemplates</bcf:option>
|
||||
<bcf:option datatype="string" backendout="1">labelalphanametemplatename</bcf:option>
|
||||
<bcf:option datatype="string" backendout="1">uniquenametemplatename</bcf:option>
|
||||
<bcf:option datatype="string" backendout="1">namehashtemplatename</bcf:option>
|
||||
<bcf:option datatype="string" backendout="1">sortingnamekeytemplatename</bcf:option>
|
||||
<bcf:option datatype="string">uniquename</bcf:option>
|
||||
<bcf:option datatype="boolean" backendout="1">familyinits</bcf:option>
|
||||
|
|
@ -1059,6 +1064,13 @@
|
|||
<bcf:namepart order="2" base="1">family</bcf:namepart>
|
||||
<bcf:namepart order="3">given</bcf:namepart>
|
||||
</bcf:uniquenametemplate>
|
||||
<!-- NAME HASH TEMPLATES -->
|
||||
<bcf:namehashtemplate name="global">
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||||
<bcf:namepart order="1" hashscope="full">family</bcf:namepart>
|
||||
<bcf:namepart order="2" hashscope="full">given</bcf:namepart>
|
||||
<bcf:namepart order="3" hashscope="full">prefix</bcf:namepart>
|
||||
<bcf:namepart order="4" hashscope="full">suffix</bcf:namepart>
|
||||
</bcf:namehashtemplate>
|
||||
<!-- SORTING NAME KEY TEMPLATES -->
|
||||
<bcf:sortingnamekeytemplate name="global" visibility="sort">
|
||||
<bcf:keypart order="1">
|
||||
|
|
|
|||
|
|
@ -1,9 +0,0 @@
|
|||
[0] Config.pm:307> INFO - This is Biber 2.19
|
||||
[0] Config.pm:310> INFO - Logfile is 'main.blg'
|
||||
[57] biber:340> INFO - === to. april 16, 2026, 22:39:11
|
||||
[68] Biber.pm:419> INFO - Reading 'main.bcf'
|
||||
[113] Biber.pm:979> INFO - Found 0 citekeys in bib section 0
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||||
[125] bbl.pm:660> INFO - Writing 'main.bbl' with encoding 'UTF-8'
|
||||
[125] bbl.pm:763> INFO - Output to main.bbl
|
||||
[125] Biber.pm:131> WARN - The file 'main.bcf' does not contain any citations!
|
||||
[125] Biber.pm:133> INFO - WARNINGS: 1
|
||||
471
latex/main.fdb_latexmk
Normal file
471
latex/main.fdb_latexmk
Normal file
|
|
@ -0,0 +1,471 @@
|
|||
# Fdb version 4
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||||
["biber main"] 1777413664.77049 "main.bcf" "main.bbl" "main" 1777413923.53173 0
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||||
"main.bcf" 1777413923 108158 63065a388e3e97b23993b45f7d78c2e4 "pdflatex"
|
||||
(generated)
|
||||
"main.bbl"
|
||||
"main.blg"
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||||
(rewritten before read)
|
||||
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"C:/Users/gabri/AppData/Local/Programs/MiKTeX/tex/latex/pgf/systemlayer/pgfsys.sty" 1756451144 443 8c872229db56122037e86bcda49e14f3 ""
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"C:/Users/gabri/AppData/Local/Programs/MiKTeX/tex/latex/pgf/utilities/pgffor.sty" 1756451144 348 ee405e64380c11319f0e249fed57e6c5 ""
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"C:/Users/gabri/AppData/Local/Programs/MiKTeX/tex/latex/pgf/utilities/pgfkeys.sty" 1756451144 274 5ae372b7df79135d240456a1c6f2cf9a ""
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"C:/Users/gabri/AppData/Local/Programs/MiKTeX/tex/latex/pgf/utilities/pgfrcs.sty" 1756451144 325 f9f16d12354225b7dd52a3321f085955 ""
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"C:/Users/gabri/AppData/Local/Programs/MiKTeX/tex/latex/psnfss/helvet.sty" 1585926771 1558 de0ad166b701b820e03588a29bb30798 ""
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"C:/Users/gabri/AppData/Local/Programs/MiKTeX/tex/latex/psnfss/t1phv.fd" 1585253778 1536 47067fbe7c3ffed1ede7aaa7b8549d7a ""
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"C:/Users/gabri/AppData/Local/Programs/MiKTeX/tex/latex/refcount/refcount.sty" 1576433952 9878 9e94e8fa600d95f9c7731bb21dfb67a4 ""
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"C:/Users/gabri/AppData/Local/Programs/MiKTeX/tex/latex/titlesec/titlesec.sty" 1736608268 48766 87a17a4ef312a39cd43896e34a679a56 ""
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"C:/Users/gabri/AppData/Local/Programs/MiKTeX/tex/latex/tocloft/tocloft.sty" 1578908763 37263 3e78d14f0f4b1a30560fea5e04de805d ""
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"C:/Users/gabri/AppData/Local/Programs/MiKTeX/tex/latex/tools/calc.sty" 1761901070 10374 2ffd4f27c7f90b8a300608069537743c ""
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"C:/Users/gabri/AppData/Local/Programs/MiKTeX/tex/latex/url/url.sty" 1388490452 12796 8edb7d69a20b857904dd0ea757c14ec9 ""
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"C:/Users/gabri/AppData/Local/Programs/MiKTeX/tex/latex/xcolor/xcolor.sty" 1729265222 55384 b454dec21c2d9f45ec0b793f0995b992 ""
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"Illustrations/Q40100.png" 1777413663 25534 3903b768afac79c9e7d517e7687745b5 ""
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"Illustrations/Q40200.png" 1777413663 26122 48e5389e3f876002f7623157a4d40d18 ""
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"Illustrations/Q40400.png" 1777413663 26211 018ca24635410e65af115ba0f490feb2 ""
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"Illustrations/Q4eigenValTEMPSCONT.png" 1777413663 15227 e754bab7bf6e601b2be0bd90e15777ec ""
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"Illustrations/Q5stepReponse.png" 1777413663 24823 a0cf1d78769249bde4a7e7a568957008 ""
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"Questions/Q1.tex" 1777413663 700 70c41b92f149e8cd6dac2ab3015d1e31 ""
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"Questions/Q2.tex" 1777413663 1519 f45ac94953f36d7a280ae237779fcfb8 ""
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"Questions/Q3.tex" 1777413663 1352 a257c83e8bc12f43a3ad444b544f413e ""
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"Questions/Q4.tex" 1777413663 1541 0935f98ad49c015cf6c870793f824b38 ""
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"Questions/Q5.tex" 1777413918 356 c4396989f5aaa32f8a97151713691918 ""
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"c:/Users/gabri/OneDrive/Área de Trabalho/BE/BE_CommandeNum/latex/main.tex" 1777413664 2229 2f59aa770f940eacbb25ee30c90b002d ""
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"contents.tex" 1777413901 1065 6048681eef6085bc8801b7e931ec307e ""
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"main.aux" 1777413923 1467 de105c5c37a18efc54d80323567d081e "pdflatex"
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"main.bbl" 1777413667 486 76d65a242ec496c9b4361af646ff12cb "biber main"
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"main.mtc" 1777413921 0 d41d8cd98f00b204e9800998ecf8427e "pdflatex"
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"main.mtc0" 1777413921 0 d41d8cd98f00b204e9800998ecf8427e "pdflatex"
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"main.out" 1777413923 852 354f0dcbcc670dc0a8e06c27477f2123 "pdflatex"
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"main.run.xml" 1777413923 2315 82c017210b861cce18c0ee8a62afc626 "pdflatex"
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"main.stc1" 1777413922 0 d41d8cd98f00b204e9800998ecf8427e "pdflatex"
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"main.stc2" 1777413922 334 9e7b0e2fe559a12aa13a73fc4886abc3 "pdflatex"
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"main.tex" 1777413664 2229 2f59aa770f940eacbb25ee30c90b002d ""
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"main.toc" 1777413923 386 d0fa34234a4de19f2c73c75cac537d36 "pdflatex"
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"template/assets/carre.png" 1777365311 99 c1d702877dec6be352f68c158a974516 ""
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"template/assets/template_first_page.pdf" 1777365311 63621 388289c61fc94f165f3c9846781d9abf ""
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"template/assets/template_last_page.pdf" 1777365311 14578 84fc0315f3d08c932e360ce6d3f7c7e6 ""
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"template/assets/template_page.pdf" 1777365311 1630 9a32997468c02dff8c3ad4ac53207b6a ""
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"template/derniere_page.tex" 1777365311 1356 c801381dbc8a2beb3b7d79031b1cde74 ""
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"template/preambule.tex" 1777365311 1649 2f4b798e0395f4c1f20f29e2163e3898 ""
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"template/premiere_page.tex" 1777365311 1032 8faf115fd2eeab692e665f596a025db4 ""
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"template/table_des_matieres.tex" 1777365311 214 2a7067bdeea73b4629f3408caff945e8 ""
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(generated)
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\contentsline {figure}{\numberline {1}{\ignorespaces Ceci est un exemple de figure.}}{2}{figure.1}%
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\babel@toc {french}{}\relax
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\contentsline {table}{\numberline {1}{\ignorespaces Ceci est un exemple de tableau.}}{2}{table.1}%
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\BOOKMARK [1][-]{section*.1}{\376\377\000I\000n\000t\000r\000o\000d\000u\000c\000t\000i\000o\000n}{}% 1
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\BOOKMARK [1][-]{section.1}{\376\377\000D\000y\000n\000a\000m\000i\000q\000u\000e\000\040\000d\000u\000\040\000s\000y\000s\000t\000\350\000m\000e\000\040\000a\000v\000e\000c\000\040\000\351\000q\000u\000a\000t\000i\000o\000n\000s\000\040\000d\000i\000f\000f\000e\000r\000e\000n\000t\000i\000e\000l\000l\000e\000s\000\040\000p\000a\000r\000t\000i\000e\000l\000l\000e\000s}{}% 2
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\BOOKMARK [1][-]{section.1}{\376\377\000D\000y\000n\000a\000m\000i\000q\000u\000e\000\040\000d\000u\000\040\000s\000y\000s\000t\000\350\000m\000e\000\040\000a\000v\000e\000c\000\040\000\351\000q\000u\000a\000t\000i\000o\000n\000s\000\040\000d\000i\000f\000f\000\351\000r\000e\000n\000t\000i\000e\000l\000l\000e\000s\000\040\000p\000a\000r\000t\000i\000e\000l\000l\000e\000s}{}% 2
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\BOOKMARK [2][-]{subsection.1.1}{\376\377\000E\000s\000p\000a\000c\000e\000\040\000d\000'\000\351\000t\000a\000t}{section.1}% 3
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\BOOKMARK [1][-]{section.2}{\376\377\000U\000n\000e\000\040\000a\000u\000t\000r\000e\000\040\000s\000e\000c\000t\000i\000o\000n}{}% 4
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\BOOKMARK [1][-]{section.3}{\376\377\000A\000n\000o\000t\000h\000e\000r\000\040\000s\000e\000c\000t\000i\000o\000n}{}% 5
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\BOOKMARK [2][-]{subsection.3.1}{\376\377\000U\000n\000e\000\040\000s\000o\000u\000s\000\040\000s\000e\000c\000t\000i\000o\000n}{section.3}% 6
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\BOOKMARK [1][-]{section*.2}{\376\377\000C\000o\000n\000c\000l\000u\000s\000i\000o\000n}{}% 8
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\BOOKMARK [2][-]{subsection.1.2}{\376\377\000D\000i\000s\000c\000r\000\351\000t\000i\000s\000a\000t\000i\000o\000n\000\040\000p\000a\000r\000\040\000\351\000l\000\351\000m\000e\000n\000t\000s\000\040\000f\000i\000n\000i\000s}{section.1}% 4
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{\reset@font\stcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {1.1}Espace d'état}{\reset@font\stcSSfont 2}{subsection.1.1}}
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{\reset@font\stcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {1.2}Discrétisation par éléments finis}{\reset@font\stcSSfont 2}{subsection.1.2}}
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{\reset@font\stcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {3.1}Une sous section}{\reset@font\stcSSfont 4}{subsection.3.1}}
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{\reset@font\stcSSSfont\mtc@string\contentsline{subsubsection}{\noexpand \leavevmode \numberline {3.1.1}Une sous sous section}{\reset@font\stcSSSfont 4}{subsubsection.3.1.1}}
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{\reset@font\stcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {3.2}Discrétisation par éléments finis}{\reset@font\stcSSfont 4}{subsection.3.2}}
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{\reset@font\stcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {1.2}Discrétisation par éléments finis}{\reset@font\stcSSfont 2}{subsection.1.2}}
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\renewcommand{\familydefault}{\sfdefault} % Si vous voulez passer en Arial le texte
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||||
\newcommand{\titre}{Nom du document}
|
||||
\newcommand{\imagecouverture}{example-image}
|
||||
\newcommand{\titre}{\hspace*{2.2cm}BE Commande Numerique}
|
||||
\newcommand{\imagecouverture}{example-image} %%HOW TO TAKE THIS SHIT OFF
|
||||
\newcommand{\firstcouverture}{
|
||||
\parbox{\textwidth}{
|
||||
\sffamily % arial
|
||||
\textbf{Prénom NOM}\\
|
||||
Elève Ingénieur de l'INSA Toulouse\\
|
||||
Département XX\\
|
||||
Spécialité TLS-SEC\\
|
||||
Promotion XX\\
|
||||
20XX-20XX
|
||||
\textbf{Brage JOHNSEN}\\
|
||||
\textbf{Gabriela DONZELLI}\\
|
||||
\textbf{Thibaut ALETRUT}\\
|
||||
Département GEI\\
|
||||
4A-AE\\
|
||||
}
|
||||
}
|
||||
\newcommand{\secondcouverture}{
|
||||
|
|
@ -37,6 +36,11 @@
|
|||
}
|
||||
}
|
||||
|
||||
%subplot
|
||||
\usepackage{subcaption}
|
||||
\usepackage{float}
|
||||
\usepackage{graphicx}
|
||||
|
||||
% bibliographie
|
||||
\usepackage{biblatex}
|
||||
\addbibresource{contents/bibliography.bib}
|
||||
|
|
|
|||
|
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@ -1,9 +1,5 @@
|
|||
\babel@toc {french}{}\relax
|
||||
\contentsline {section}{Introduction}{1}{section*.1}%
|
||||
\contentsline {section}{\numberline {1}Dynamique du système avec équations differentielles partielles}{2}{section.1}%
|
||||
\contentsline {section}{\numberline {1}Dynamique du système avec équations différentielles partielles}{2}{section.1}%
|
||||
\contentsline {subsection}{\numberline {1.1}Espace d'état}{2}{subsection.1.1}%
|
||||
\contentsline {section}{\numberline {2}Une autre section}{3}{section.2}%
|
||||
\contentsline {section}{\numberline {3}Another section}{4}{section.3}%
|
||||
\contentsline {subsection}{\numberline {3.1}Une sous section}{4}{subsection.3.1}%
|
||||
\contentsline {subsubsection}{\numberline {3.1.1}Une sous sous section}{4}{subsubsection.3.1.1}%
|
||||
\contentsline {section}{Conclusion}{5}{section*.2}%
|
||||
\contentsline {subsection}{\numberline {1.2}Discrétisation par éléments finis}{2}{subsection.1.2}%
|
||||
|
|
|
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Loading…
Reference in a new issue