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Tournesol02 2026-04-28 16:25:29 +02:00
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@ -4,9 +4,16 @@ Une introduction
\newpage
\section{Dynamique du système avec équations differentielles partielles}
\subsection{Espace d'état}
L'espace d'état se trouve sous la forme:
\textbf{Question 1}
L'espace d'état se trouve sous la forme:
\begin{center}
\begin{equation}
\rho(\zeta)\frac{\partial^2 w}{\partial t^2}(\zeta,t) = -\frac{\partial^2}{\partial \zeta ^2}\begin{bmatrix}
EI(\zeta )\frac{\partial^2}{\partial \zeta^2}(\zeta,t)
\end{bmatrix}
-q(\zeta,t)
\end{equation}
$E =$
\[
\begin{bmatrix}
@ -16,9 +23,47 @@ $E =$
-13/420 & -11/210 & -1/140 & 1/105
\end{bmatrix}
\]
\end{center}
\begin{equation}
x_1(\zeta,t)=\frac{\partial^2 w}{\partial \zeta ^2}(\zeta,t) \;
x_2(\zeta,t)=\rho(\zeta)\frac{\partial w}{\partial t}(\zeta,t)
\end{equation}
Salut Thibo
\begin{equation}
e_1(\zeta,t)=EI(\zeta)x_1(\zeta,t) \;
e_2(\zeta,t)=\frac{1}{\rho(\zeta)}x_2(\zeta,t)
\end{equation}
\begin{equation}
\dot{x}(t)=\begin{bmatrix}
\dot{x}_1 \\
\dot{x}_2
\end{bmatrix}
= \frac{\partial^2}{\partial z^2}
\begin{bmatrix}
0 & 1 \\
-1 & 0
\end{bmatrix}
\begin{bmatrix}
e_1(\zeta,t) & e_2(\zeta ,t)
\end{bmatrix}
+
\begin{bmatrix}
0 \\
-q(\zeta,t)
\end{bmatrix}
\end{equation}
\end{center}
Voici la represntation d'état à partir des equations diferentielles.
\textbf{Question 2}
Comment ajouter un image:
\includegraphics[scale=1]{./Illustrations/im1.png}
Les Poles du système avec retour d'état.
\section{Une autre section}
\begin{figure}[h]

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