diff options
Diffstat (limited to 'buch/chapters/60-gruppen/images/phasenraum.tex')
-rw-r--r-- | buch/chapters/60-gruppen/images/phasenraum.tex | 186 |
1 files changed, 93 insertions, 93 deletions
diff --git a/buch/chapters/60-gruppen/images/phasenraum.tex b/buch/chapters/60-gruppen/images/phasenraum.tex index 2305b26..2bccc27 100644 --- a/buch/chapters/60-gruppen/images/phasenraum.tex +++ b/buch/chapters/60-gruppen/images/phasenraum.tex @@ -1,93 +1,93 @@ -%
-% 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]
-
-\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 {0.5,1,...,6}{
- \draw plot[domain=0:359,samples=360]
- ({\r*cos(\x)},{\o*\r*sin(\x)}) -- cycle;
-}
-
-\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}
-
- \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}
- }
-}
-
-%\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}
-
+% +% 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] + +\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 {0.5,1,...,6}{ + \draw plot[domain=0:359,samples=360] + ({\r*cos(\x)},{\o*\r*sin(\x)}) -- cycle; +} + +\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} + + \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} + } +} + +%\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} + |