Merge pull request #48 from samnied/master

Abgabe zur Korrektur

3 files changed, 187 insertions, 0 deletions

diff --git a/buch/papers/kra/images/multi_mass_spring.tex b/buch/papers/kra/images/multi_mass_spring.tex
new file mode 100644
index 0000000..f255cc8
--- /dev/null
+++ b/buch/papers/kra/images/multi_mass_spring.tex
@@ -0,0 +1,54 @@
+% create tikz drawing of a multi mass multi spring system
+
+\tikzstyle{vmline}=[red, dashed,line width=0.4,dash pattern=on 1pt off 1pt]
+\tikzstyle{ground}=[pattern=north east lines]
+\tikzstyle{mass}=[line width=0.6,red!30!black,fill=red!40!black!10,rounded corners=1,top color=red!40!black!20,bottom color=red!40!black!10,shading angle=20]
+\tikzstyle{spring}=[line width=0.8,blue!7!black!80,snake=coil,segment amplitude=5,line cap=round]
+
+\begin{tikzpicture}[scale=2]
+    \newcommand{\ticks}[3]
+    {
+        % x, y coordinates
+        \draw[thick] (#1, #2 - 0.1 / 2) --++ (0, 0.1) node[scale=0.8,below=0.2] {#3};
+    }
+    \tikzmath{
+        \hWall = 1.2;
+        \wWall = 0.3;
+        \lWall = 5;
+        \hMass = 0.6;
+        \wMass = 1.1;
+        \xMass1 = 1.0;
+        \xMass2 = 3.0;
+        \xAxisYpos = 0;
+        \originX1 = 0;
+        \originY1 = 0.5;
+        \springscale=7;
+    }
+
+    % create axis
+    \draw[->,thick] (0,\xAxisYpos) --+ (\xMass2 + \wMass, 0) node[right]{$q$};
+    % create ticks on x / q axis
+    \ticks{\xMass1}{\xAxisYpos}{$q_{1}$}
+    \ticks{\xMass2}{\xAxisYpos}{$q_{2}$}
+
+    % create non-moving backgrounds
+    \draw[ground] (\originX1, \originY1) ++ (0, 0) --+(\lWall,0) --+(\lWall, \hWall)
+    --+ (\lWall - \wWall, \hWall) --+(\lWall - \wWall, \wWall) --+ (\wWall, \wWall)  --+(\wWall, \hWall) --+(0, \hWall) -- cycle;
+
+    % create masses
+    \draw[mass] (\originX1, \originY1) ++ (\xMass1, \wWall) rectangle ++ (\wMass,\hMass) node[midway] {$m_{1}$};
+    \draw[mass] (\originX1, \originY1) ++ (\xMass2, \wWall) rectangle ++ (\wMass,\hMass) node[midway] {$m_{2}$};
+
+    % create springs
+    \draw[spring, segment length=(\xMass1 - \wWall) * \springscale] (\originX1, \originY1) ++
+    (\wWall, \wWall + \hMass / 2) --++ (\xMass1 - \wWall, 0) node[midway,above=0.2] {$k_1$};
+    \draw[spring, segment length=(\xMass1 - \wWall) * \springscale] (\originX1, \originY1) ++
+    (\xMass1 + \wMass, \wWall + \hMass / 2) --++ (\xMass2 - \xMass1 - \wMass, 0) node[midway,above=0.2] {$k_c$};
+    \draw[spring, segment length=(\xMass1 - \wWall) * \springscale] (\originX1, \originY1) ++
+    (\xMass2 + \wMass, \wWall + \hMass / 2) --++ (\lWall - \xMass2 - \wMass - \wWall, 0) node[midway,above=0.2] {$k_2$};
+
+    % create vertical measurement line 
+    \draw[vmline] (\xMass1, \xAxisYpos) --+(0, \originY1 + \wWall);
+    \draw[vmline] (\xMass2, \xAxisYpos) --+(0, \originY1 + \wWall);
+
+\end{tikzpicture}
diff --git a/buch/papers/kra/images/phase_space.tex b/buch/papers/kra/images/phase_space.tex
new file mode 100644
index 0000000..cd51ea4
--- /dev/null
+++ b/buch/papers/kra/images/phase_space.tex
@@ -0,0 +1,67 @@
+\colorlet{mypurple}{red!50!blue!90!black!80}
+
+% style to create arrows
+\tikzset{
+    traj/.style 2 args={thick, postaction={decorate},decoration={markings,
+                    mark=at position #1 with {\arrow{<}},
+                    mark=at position #2 with {\arrow{<}}}
+        }
+}
+
+\begin{tikzpicture}[scale=0.6]
+    % p(t=0) = 0, q(t=0) = A, max(p) = mwA
+    \tikzmath{
+        \axh = 5.2;
+        \axw1 = 4.2;
+        \axw2 = 4.8;
+        \d1 = 0.9;
+        \a0 = 1;
+        \b0 = 2;
+        \a1 = \a0 + \d1;
+        \b1 = \b0 + \d1;
+        \a2 = \a1 + \d1;
+        \b2 = \b1 + \d1;
+        \a3 = \a2 + \d1;
+        \b3 = \b2 + \d1;
+        \d2 = 0.75;
+        \aa0 = 2;
+        \bb0 = 1;
+        \aa1 = \aa0 + \d2;
+        \bb1 = \bb0 + \d2;
+        \aa2 = \aa1 + \d2;
+        \bb2 = \bb1 + \d2;
+        \aa3 = \aa2 + \d2;
+        \bb3 = \bb2 + \d2;
+    }
+
+    \draw[->,thick] (-\axw1,0) -- (\axw1,0) node[right] {$q$};
+    \draw[->,thick] (0,-\axh) -- (0,\axh) node[above] {$p$};
+
+    \draw[traj={0.375}{0.875},darkgreen] ellipse (\a0 and \b0);
+    \draw[traj={0.375}{0.875},blue] ellipse (\a1 and \b1);
+    \draw[traj={0.375}{0.875},cyan] ellipse (\a2 and \b2);
+    \draw[traj={0.375}{0.875},mypurple] ellipse (\a3 and \b3);
+
+    \node[right,darkgreen] at (45:{\a0} and {\b0}) {$E_A$};
+    \node[right, blue] at (45:{\a1} and {\b1}) {$E_B$};
+    \node[right, cyan] at (45:{\a2} and {\b2}) {$E_C$};
+    \node[right, mypurple] at (45:{\a3} and {\b3}) {$E_D$};
+    \node[above left] at (110:\b3 + 0.1) {grosses $\omega$};
+
+    \begin{scope}[xshift=12cm]
+        \draw[->,thick] (-\axw2,0) -- (\axw2,0) node[right] {$q$};
+        \draw[->,thick] (0,-\axh) -- (0,\axh) node[above] {$p$};
+
+        \draw[traj={0.375}{0.875},darkgreen] ellipse (\aa0 and \bb0);
+        \draw[traj={0.375}{0.875},blue] ellipse (\aa1 and \bb1);
+        \draw[traj={0.375}{0.875},cyan] ellipse (\aa2 and \bb2);
+        \draw[traj={0.375}{0.875},mypurple] ellipse (\aa3 and \bb3);
+
+        \node[above, darkgreen] at (45:{\aa0} and {\bb0}) {$E_A$};
+        \node[above, blue] at (45:{\aa1} and {\bb1}) {$E_B$};
+        \node[above, cyan] at (45:{\aa2} and {\bb2}) {$E_C$};
+        \node[above, mypurple] at (45:{\aa3} and {\bb3}) {$E_D$};
+
+        \node[above left] at (110:\b3 + 0.1) {kleines $\omega$};
+    \end{scope}
+\end{tikzpicture}
\ No newline at end of file
diff --git a/buch/papers/kra/images/simple_mass_spring.tex b/buch/papers/kra/images/simple_mass_spring.tex
new file mode 100644
index 0000000..e0e869a
--- /dev/null
+++ b/buch/papers/kra/images/simple_mass_spring.tex
@@ -0,0 +1,66 @@
+% create tikz drawing of a simple mass spring system
+
+\tikzstyle{hmline}=[{Latex[length=3.3,width=2.2]}-{Latex[length=3.3,width=2.2]},line width=0.3]
+\tikzstyle{vmline}=[red, dashed,line width=0.4,dash pattern=on 1pt off 1pt]
+\tikzstyle{ground}=[pattern=north east lines]
+\tikzstyle{mass}=[line width=0.6,red!30!black,fill=red!40!black!10,rounded corners=1,top color=red!40!black!20,bottom color=red!40!black!10,shading angle=20]
+\tikzstyle{spring}=[line width=0.8,blue!7!black!80,snake=coil,segment amplitude=5,line cap=round]
+
+\begin{tikzpicture}[scale=2]
+    \newcommand{\ticks}[2]
+    {
+        % arguments: x, y coordinates
+        \draw[thick] (#1, #2 - 0.1 / 2) --++ (0, 0.1);
+    }
+
+    \tikzmath{
+        \hWall = 1.2;
+        \wWall = 0.3;
+        \lWall = 3.5;
+        \hMass = 0.6;
+        \wMass = 1.1;
+        \xMass1 = 1.2;
+        \xMass2 = 2.2;
+        \xAxisYpos = 0;
+        \originX1 = 0;
+        \originY1 = 0.5;
+        \originX2 = 0;
+        \originY2 = -2;
+        \springscale=7;
+    }
+
+    % create x axis
+    \draw[->,thick] (0,\xAxisYpos) --+ (\lWall, 0) node[right]{$x$};
+
+    % create ticks on x axis
+    \ticks{\wWall}{\xAxisYpos}
+    \ticks{\xMass1}{\xAxisYpos}
+    \ticks{\xMass2}{\xAxisYpos}
+
+    % create underground
+    \draw[ground] (\originX1, \originY1) ++ (0, 0) --+(\lWall,0) --+(\lWall, \wWall) --+(\wWall, \wWall) --+(\wWall, \hWall) --+(0, \hWall) -- cycle;
+    \draw[ground] (\originX2, \originY2) ++ (0, 0) --+(\lWall,0) --+(\lWall, \wWall) --+(\wWall, \wWall) --+(\wWall, \hWall) --+(0, \hWall) -- cycle;
+
+    % create masses
+    \draw[mass] (\originX1, \originY1) ++ (\xMass1, \wWall) rectangle ++ (\wMass,\hMass) node[midway] {$m$};
+    \draw[mass] (\originX2, \originY2) ++ (\xMass2, \wWall) rectangle ++ (\wMass,\hMass) node[midway] {$m$};
+
+    % create springs
+    \draw[spring, segment length=(\xMass1 - \wWall) * \springscale] (\originX1, \originY1) ++
+    (\wWall, \wWall + \hMass / 2) --++ (\xMass1 - \wWall, 0) node[midway,above=0.2] {$k$};
+    \draw[spring, segment length=(\xMass2 - \wWall) * \springscale] (\originX2, \originY2) ++
+    (\wWall, \wWall + \hMass / 2) --++ (\xMass2 - \wWall, 0) node[midway,above=0.2] {$k$};
+
+    % create vertical measurement line 
+    \draw[vmline] (\xMass1, \xAxisYpos) --+(0, \originY1 + \wWall);
+    \draw[vmline] (\xMass2, \xAxisYpos) --+(0, \originY2 + \hMass+\wWall);
+    \draw[vmline] (\wWall, \originY1+\wWall) --(\wWall, \originY2 + \hWall);
+
+    % create horizontal measurement line
+    \draw[hmline] (\wWall, \xAxisYpos + 0.2) -- (\xMass1, \xAxisYpos + 0.2) node[midway,fill=white,inner sep=0] {$\ell_0$};
+    \draw[hmline] (\xMass1, \xAxisYpos + 0.2) -- (\xMass2, \xAxisYpos + 0.2) node[midway,fill=white,inner sep=0] {$\Delta_{x}$};
+    \draw[hmline] (\wWall, \xAxisYpos - 0.3) -- (\xMass2, \xAxisYpos - 0.3) node[midway,fill=white,inner sep=0] {$\ell_{1}$};
+
+    %  create force arrow
+    \draw[->,blue, very thick,line cap=round] (\xMass2 + \wMass / 2, \originY2 + \wWall + \hMass + 0.15) node[above] {$\vb{F_{R}}$} --+ (-0.5, 0);
+\end{tikzpicture}
\ No newline at end of file