111 lines
4.7 KiB
TeX
111 lines
4.7 KiB
TeX
\documentclass{article}
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\usepackage{cours}
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\usepackage{lipsum}
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\title{\bfseries Cours}
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\author{Edgar P. Burkhart}
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\begin{document}
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\maketitle
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\tableofcontents
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\section{AH}
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\subsection{Ah}
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\subsubsection{ah}
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\paragraph{Paragraphe §1} \lipsum[1]{} On a donc $L=\SI{23.556}{\kg\per\square\m\s}$, soit \SI{+3.14e2}{\newton\meter\per\watt} de \ce{CO2}, comme démontré en \autoref{eq:1} (Cf \autoref{fig:case}).
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\begin{equation}
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\int\sum x^n\sin y-1\label{eq:1}
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\end{equation}
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\begin{lstlisting}[language=python]
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def f(x, n, y):
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if x>=0:
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return int(sum(x**n*sin(y)))-1
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return 0
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\end{lstlisting}
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\begin{figure}
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\centering
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\begin{subfigure}{\linewidth}
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\centering
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\begin{tikzpicture}[scale=2,
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cote/.style={|<->|, gray},
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mesh/.style={dashed, gray},
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]
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\fill[blue!20] (0,0) rectangle (1,0.4);
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\fill[blue!20] (1.05,0.2) rectangle (2.55,0) rectangle (6,0.1);
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\draw (0,0) node[below left]{0} -- (1,0) node[below left]{1} -- (1,0.4) node[below left]{5} -- (1.05,0.4) node[below right]{6} -- (1.05,0) node[below right]{2} -- (6,0) node[below right]{3} -- (6,0.4) node[right]{7} -- (6,0.6) node[above right]{11} -- (1.05,0.6) node[above right]{10} -- (1,0.6) node[above left]{9} -- (0,0.6) node[above left]{8} -- (0,0.4) node[left]{4} -- cycle;
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\draw[mesh] (0,0.4) -- (1,0.4) -- (1,0.6);
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\draw[mesh] (6,0.4) -- (1.05,0.4) -- (1.05,0.6);
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\draw[cote] (0,-0.35) -- ++(1,0) node[midway, below]{\SI{1}{\m}};
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\draw[gray, |-|] (1,-0.35) -- ++(0.05,0) node[midway, below]{\SI{5}{\cm}};
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\draw[cote] (1.05,-0.35) -- ++(1.5,0) node[midway, below]{\SI{1.5}{\m}};
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\draw[cote] (0,-0.25) -- ++(6,0) node[midway, below]{\SI{6}{\m}};
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\draw[cote] (0.3,0) -- ++(0,.4) node[midway, left]{$h_0$} node[midway, right]{\SI{40}{\cm}};
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\draw[cote] (2,0) -- ++(0,.2) node[midway, left]{\SI{20}{\cm}};
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\draw[cote] (4,0) -- ++(0,.1) node[midway, above left]{\SI{10}{\cm}};
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\draw[cote] (-0.25,0) -- ++(0,.6) node[midway, left]{\SI{60}{\cm}};
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\end{tikzpicture}
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\caption{Initial configuration.}\label{fig:dbd}
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\end{subfigure}
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\begin{subfigure}{\linewidth}
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\centering
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\begin{tikzpicture}[scale=2,
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cote/.style={|<->|, gray},
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mesh/.style={dashed, gray},
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]
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\fill[blue!20] (0,0) rectangle (1,0.6);
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\fill[blue!20] (1.01,0.2) rectangle (2.51,0) rectangle (6,0.1);
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\draw (0,0) node[below left]{0} -- (1,0) node[below left]{1} -- (1,0.6) node[below left]{5} -- (1.01,0.6) node[below right]{6} -- (1.01,0) node[below right]{2} -- (6,0) node[below right]{3} -- (6,0.6) node[right]{7} -- (6,0.8) node[above right]{11} -- (1.01,0.8) node[above right]{10} -- (1,0.8) node[above left]{9} -- (0,0.8) node[above left]{8} -- (0,0.6) node[left]{4} -- cycle;
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\draw[mesh] (0,0.6) -- (1,0.6) -- (1,0.8);
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\draw[mesh] (6,0.6) -- (1.01,0.6) -- (1.01,0.8);
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\draw[cote] (0,-0.35) -- ++(1,0) node[midway, below]{\SI{1}{\m}};
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\draw[gray, |-|] (1,-0.35) -- ++(0.01,0) node[midway, below]{\SI{1}{\cm}};
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\draw[cote] (1.01,-0.35) -- ++(1.5,0) node[midway, below]{\SI{1.5}{\m}};
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\draw[cote] (0,-0.25) -- ++(6,0) node[midway, below]{\SI{6}{\m}};
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\draw[cote] (0.3,0) -- ++(0,.6) node[midway, left]{$h_0$} node[midway, right]{\SI{60}{\cm}};
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\draw[cote] (2,0) -- ++(0,.2) node[midway, left]{\SI{20}{\cm}};
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\draw[cote] (4,0) -- ++(0,.1) node[midway, above left]{\SI{10}{\cm}};
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\draw[cote] (-0.25,0) -- ++(0,.8) node[midway, left]{\SI{80}{\cm}};
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\end{tikzpicture}
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\caption{Adjusted configuration.}\label{fig:dbda}
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\end{subfigure}
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\caption{Studied case.}\label{fig:case}
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\end{figure}
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$$\scriptsize
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\begin{bmatrix}
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\ddot q_1 & sin(q_2)^2\ddot q_1 + \frac{1}{2}(\dot q_2\dot q_1 sin(2q_2)+q_1 sin(2q_2)\dot q_2) & cos(q_2) \ddot q_2- \dot q_2^2 sin(q_2) & 0 & 0 & \dot q_1 & 0 & tanh(1000 \dot q_1) & 0 \\
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0 &
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- \frac{1}{2} \dot q_1^2 sin(2 q_2) &
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cos(q_2) \ddot q_1 &
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\ddot q_2 & -sin(q_2) &
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0 &
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\dot q_2 &
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0 &
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tanh(1000 \dot q_2)
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\end{bmatrix}
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$$
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$$
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\text{GridSWAN}=\begin{bmatrix}
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x_{11} & x_{12} & \dots & x_{1m} & y_{11} & y_{12} & \dots & y_{1m} \\
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x_{21} & x_{22} & \dots & x_{2m} & y_{21} & y_{22} & \dots & y_{2m} \\
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\dots & & & & & & & \dots \\
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x_{n1} & x_{n2} & \dots & x_{nm} & y_{n1} & y_{n2} & \dots & y_{nm} \\
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\end{bmatrix}
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$$
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$$
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\text{BathySWAN}=\begin{bmatrix}
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z_{11} & z_{12} & \dots & z_{1m} \\
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z_{21} & z_{22} & \dots & z_{2m} \\
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\dots & & & \dots \\
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z_{n1} & z_{n2} & \dots & z_{nm} \\
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\end{bmatrix}
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$$
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\listoffigures
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\end{document} |