From ea9c6380f729ddd512fa59c2d0b67cc7cc8ab56c Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@othello.ch>
Date: Fri, 2 Apr 2021 21:43:03 +0200
Subject: kontinuierliche Symmetrien

---
 buch/chapters/60-gruppen/images/phasenraum.tex | 45 ++++++++++++++++++++++++++
 1 file changed, 45 insertions(+)
 create mode 100644 buch/chapters/60-gruppen/images/phasenraum.tex

(limited to 'buch/chapters/60-gruppen/images/phasenraum.tex')

diff --git a/buch/chapters/60-gruppen/images/phasenraum.tex b/buch/chapters/60-gruppen/images/phasenraum.tex
new file mode 100644
index 0000000..136d91d
--- /dev/null
+++ b/buch/chapters/60-gruppen/images/phasenraum.tex
@@ -0,0 +1,45 @@
+%
+% phasenraum.tex -- 
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usetikzlibrary{arrows,intersections,math}
+\begin{document}
+\def\skala{1}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\pgfmathparse{1/sqrt(2)}
+\xdef\o{\pgfmathresult}
+
+\def\punkt#1#2{ ({#2*cos(#1)},{\o*#2*sin(#1)}) }
+
+\foreach \r in {1,2,...,6}{
+	\draw[line width=0.5pt]
+		plot[domain=0:359,samples=360]
+			({\r*cos(\x)},{\o*\r*sin(\x)}) -- cycle;
+}
+\draw[color=red,line width=1.4pt]
+	plot[domain=0:359,samples=360]
+		({4*cos(\x)},{\o*4*sin(\x)}) -- cycle;
+
+\draw[->] (-6.1,0) -- (6.3,0) coordinate[label={$x$}];
+\draw[->] (0,-4.4) -- (0,4.7) coordinate[label={right:$p$}];
+
+\node at \punkt{0}{4} [below right] {$x_0$};
+\node at \punkt{90}{4} [above left] {$\omega x_0$};
+
+\fill[color=white] \punkt{60}{4} rectangle \punkt{58}{5.9};
+
+\fill[color=red] \punkt{60}{4} circle[radius=0.08];
+\node[color=red] at \punkt{60}{4} [above right]
+	{$\begin{pmatrix}x(t)\\p(t)\end{pmatrix}$};
+
+\end{tikzpicture}
+\end{document}
+
-- 
cgit v1.2.1


From 260bd654d33b27c69b47e07217fa2212ef835fbd Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@othello.ch>
Date: Sat, 3 Apr 2021 16:53:38 +0200
Subject: add new images

---
 buch/chapters/60-gruppen/images/phasenraum.tex | 72 +++++++++++++++++++++-----
 1 file changed, 60 insertions(+), 12 deletions(-)

(limited to 'buch/chapters/60-gruppen/images/phasenraum.tex')

diff --git a/buch/chapters/60-gruppen/images/phasenraum.tex b/buch/chapters/60-gruppen/images/phasenraum.tex
index 136d91d..2bccc27 100644
--- a/buch/chapters/60-gruppen/images/phasenraum.tex
+++ b/buch/chapters/60-gruppen/images/phasenraum.tex
@@ -14,32 +14,80 @@
 \def\skala{1}
 \begin{tikzpicture}[>=latex,thick,scale=\skala]
 
-\pgfmathparse{1/sqrt(2)}
+\def\m{1}
+\def\K{0.444}
+
+\pgfmathparse{sqrt(\K/\m)}
 \xdef\o{\pgfmathresult}
 
 \def\punkt#1#2{ ({#2*cos(#1)},{\o*#2*sin(#1)}) }
 
-\foreach \r in {1,2,...,6}{
-	\draw[line width=0.5pt]
-		plot[domain=0:359,samples=360]
+\foreach \r in {0.5,1,...,6}{
+	\draw plot[domain=0:359,samples=360]
 			({\r*cos(\x)},{\o*\r*sin(\x)}) -- cycle;
 }
-\draw[color=red,line width=1.4pt]
-	plot[domain=0:359,samples=360]
-		({4*cos(\x)},{\o*4*sin(\x)}) -- cycle;
 
-\draw[->] (-6.1,0) -- (6.3,0) coordinate[label={$x$}];
-\draw[->] (0,-4.4) -- (0,4.7) coordinate[label={right:$p$}];
+\def\tangente#1#2{
+		\pgfmathparse{#2/\m}
+		\xdef\u{\pgfmathresult}
+
+		\pgfmathparse{-#1*\K}
+		\xdef\v{\pgfmathresult}
+
+		\pgfmathparse{sqrt(\u*\u+\v*\v)}
+		\xdef\l{\pgfmathresult}
 
-\node at \punkt{0}{4} [below right] {$x_0$};
-\node at \punkt{90}{4} [above left] {$\omega x_0$};
+		\fill[color=blue] (#1,#2) circle[radius=0.03];
+		\draw[color=blue,line width=0.5pt]
+			({#1-0.2*\u/\l},{#2-0.2*\v/\l})
+			--
+			({#1+0.2*\u/\l},{#2+0.2*\v/\l});
+}
+
+\foreach \x in {-6.25,-5.75,...,6.3}{
+	\foreach \y in {-4.25,-3.75,...,4.3}{
+		\tangente{\x}{\y}
+	}
+}
 
-\fill[color=white] \punkt{60}{4} rectangle \punkt{58}{5.9};
+%\foreach \x in {0.5,1,...,5.5,6}{
+%	\tangente{\x}{0}
+%	\tangente{-\x}{0}
+%	\foreach \y in {0.5,1,...,4}{
+%		\tangente{\x}{\y}
+%		\tangente{-\x}{\y}
+%		\tangente{\x}{-\y}
+%		\tangente{-\x}{-\y}
+%	}
+%}
+%\foreach \y in {0.5,1,...,4}{
+%	\tangente{0}{\y}
+%	\tangente{0}{-\y}
+%}
+
+\fill[color=white,opacity=0.7] \punkt{60}{4} rectangle \punkt{59}{5.8};
+\fill[color=white,opacity=0.7] \punkt{0}{4} rectangle \punkt{18}{4.9};
+
+\draw[->,color=red,line width=1.4pt]
+	plot[domain=0:60,samples=360]
+		({4*cos(\x)},{\o*4*sin(\x)});
+
+\draw[->] (-6.5,0) -- (6.7,0) coordinate[label={$x$}];
+\draw[->] (0,-4.5) -- (0,4.7) coordinate[label={right:$p$}];
 
 \fill[color=red] \punkt{60}{4} circle[radius=0.08];
 \node[color=red] at \punkt{60}{4} [above right]
 	{$\begin{pmatrix}x(t)\\p(t)\end{pmatrix}$};
 
+\fill[color=red] \punkt{0}{4} circle[radius=0.08];
+\node[color=red] at \punkt{0}{4} [above right]
+	{$\begin{pmatrix}x_0\\0\end{pmatrix}$};
+
+\fill[color=white] (4,0) circle[radius=0.05];
+\node at (3.9,0) [below right] {$x_0$};
+\fill (0,{\o*4}) circle[radius=0.05];
+\node at (0.1,{\o*4+0.05}) [below left] {$\omega x_0$};
+
 \end{tikzpicture}
 \end{document}
 
-- 
cgit v1.2.1

