From ea9c6380f729ddd512fa59c2d0b67cc7cc8ab56c Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= 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?= 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