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authorJoshua Baer <joshua.baer@ost.ch>2022-08-16 10:28:39 +0200
committerJoshua Baer <joshua.baer@ost.ch>2022-08-16 10:28:39 +0200
commitf3fc1867221ab08c20cbb3f21663e89a10526dcb (patch)
tree49ca3a3a863f57f2ea69025ed493ba6f35d12c36 /buch/papers/kra/images
parentsignal m draw (diff)
parentfix a typo (diff)
downloadSeminarSpezielleFunktionen-f3fc1867221ab08c20cbb3f21663e89a10526dcb.tar.gz
SeminarSpezielleFunktionen-f3fc1867221ab08c20cbb3f21663e89a10526dcb.zip
Merge branch 'master' of github.com:JODBaer/SeminarSpezielleFunktionen
Diffstat (limited to '')
-rw-r--r--buch/papers/kra/images/Makefile9
-rw-r--r--buch/papers/kra/images/multi_mass_spring.tex54
-rw-r--r--buch/papers/kra/images/phase_space.tex67
-rw-r--r--buch/papers/kra/images/simple.pdfbin0 -> 23130 bytes
-rw-r--r--buch/papers/kra/images/simple.tex24
-rw-r--r--buch/papers/kra/images/simple_mass_spring.tex66
6 files changed, 220 insertions, 0 deletions
diff --git a/buch/papers/kra/images/Makefile b/buch/papers/kra/images/Makefile
new file mode 100644
index 0000000..ef226a9
--- /dev/null
+++ b/buch/papers/kra/images/Makefile
@@ -0,0 +1,9 @@
+#
+# Makefile -- build standalone images
+#
+# (c) 2022 Prof Dr Andreas Müller
+#
+all: simple.pdf
+
+simple.pdf: simple.tex simple_mass_spring.tex
+ pdflatex simple.tex
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.pdf b/buch/papers/kra/images/simple.pdf
new file mode 100644
index 0000000..4351518
--- /dev/null
+++ b/buch/papers/kra/images/simple.pdf
Binary files differ
diff --git a/buch/papers/kra/images/simple.tex b/buch/papers/kra/images/simple.tex
new file mode 100644
index 0000000..3bdde27
--- /dev/null
+++ b/buch/papers/kra/images/simple.tex
@@ -0,0 +1,24 @@
+%
+% tikztemplate.tex -- template for standalon tikz images
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\pgfplotsset{compat=1.16}
+\usepackage[outline]{contour}
+\usepackage{csvsimple}
+\usepackage{physics}
+\usetikzlibrary{arrows,intersections,math}
+\usetikzlibrary{patterns}
+\usetikzlibrary{snakes}
+\usetikzlibrary{arrows.meta}
+\usetikzlibrary{decorations}
+\usetikzlibrary{decorations.markings}
+\begin{document}
+\input{simple_mass_spring.tex}
+\end{document}
+
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..868362d
--- /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,>=latex]
+ \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=3.5] {$k$};
+ \draw[spring, segment length=(\xMass2 - \wWall) * \springscale] (\originX2, \originY2) ++
+ (\wWall, \wWall + \hMass / 2) --++ (\xMass2 - \wWall, 0) node[midway,above=3.5] {$k$};
+
+ % 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] {$l_0$};
+ \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] {$l_{1}$};
+
+ % 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}