diff options
Diffstat (limited to 'buch/chapters/60-gruppen/images/sl2.tex')
-rw-r--r-- | buch/chapters/60-gruppen/images/sl2.tex | 292 |
1 files changed, 146 insertions, 146 deletions
diff --git a/buch/chapters/60-gruppen/images/sl2.tex b/buch/chapters/60-gruppen/images/sl2.tex index c41308c..0e44aa9 100644 --- a/buch/chapters/60-gruppen/images/sl2.tex +++ b/buch/chapters/60-gruppen/images/sl2.tex @@ -1,146 +1,146 @@ -%
-% sl2.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}
-\usepackage{csvsimple}
-\usetikzlibrary{arrows,intersections,math}
-\begin{document}
-\def\skala{1}
-\begin{tikzpicture}[>=latex,thick,scale=\skala]
-
-\definecolor{darkgreen}{rgb}{0,0.6,0}
-
-\begin{scope}[xshift=-4.5cm]
- \fill[color=blue!20]
- (1.4,0) -- (0,1.4) -- (-1.4,0) -- (0,-1.4) -- cycle;
- \fill[color=red!40,opacity=0.5]
- (1.96,0) -- (0,1) -- (-1.96,0) -- (0,-1) -- cycle;
-
- \begin{scope}
- \clip (-2.1,-2.1) rectangle (2.3,2.3);
- \draw[color=darkgreen]
- plot[domain=-1:1,samples=100]
- ({(1/1.4)*exp(\x)},{(1/1.4)*exp(-\x)});
- \draw[color=darkgreen]
- plot[domain=-1:1,samples=100]
- ({(1/1.4)*exp(\x)},{-(1/1.4)*exp(-\x)});
- \draw[color=darkgreen]
- plot[domain=-1:1,samples=100]
- ({-(1/1.4)*exp(\x)},{(1/1.4)*exp(-\x)});
- \draw[color=darkgreen]
- plot[domain=-1:1,samples=100]
- ({-(1/1.4)*exp(\x)},{-(1/1.4)*exp(-\x)});
- \end{scope}
-
- \draw[->] (-2.1,0) -- (2.3,0) coordinate[label={$x$}];
- \draw[->] (0,-2.1) -- (0,2.3) coordinate[label={right:$y$}];
-
- \draw[->,color=blue] (0,0) -- (1.4,0);
- \draw[->,color=blue] (0,0) -- (0,1.4);
-
- \draw[->,color=red] (0,0) -- (1.96,0);
- \draw[->,color=red] (0,0) -- (0,1);
- \node at (0,-3.2)
- {$\displaystyle
- \begin{aligned}
- A&=\begin{pmatrix}1&0\\0&-1\end{pmatrix}
- \\
- e^{At}
- &=\begin{pmatrix}e^t&0\\0&e^{-t}\end{pmatrix}
- \end{aligned}
- $};
-
-\end{scope}
-
-
-\begin{scope}
- \fill[color=blue!20]
- (0:1.4) -- (90:1.4) -- (180:1.4) -- (270:1.4) -- cycle;
- \fill[color=red!40,opacity=0.5]
- (33:1.4) -- (123:1.4) -- (213:1.4) -- (303:1.4) -- cycle;
-
- \draw[color=darkgreen] (0,0) circle[radius=1.4];
-
- \draw[->] (-2.1,0) -- (2.3,0) coordinate[label={$x$}];
- \draw[->] (0,-2.1) -- (0,2.3) coordinate[label={right:$y$}];
-
- \draw[->,color=blue] (0,0) -- (1.4,0);
- \draw[->,color=blue] (0,0) -- (0,1.4);
-
- \draw[->,color=red] (0,0) -- (33:1.4);
- \draw[->,color=red] (0,0) -- (123:1.4);
-
- \node at (0,-3.2)
- {$\displaystyle
- \begin{aligned}
- B
- &=\begin{pmatrix}0&-1\\1&0 \end{pmatrix}
- \\
- e^{Bt}
- &=
- \begin{pmatrix}
- \cos t&-\sin t\\
- \sin t& \cos t
- \end{pmatrix}
- \end{aligned}$};
-\end{scope}
-
-
-\begin{scope}[xshift=4.5cm]
- \fill[color=blue!20]
- (0:1.4) -- (90:1.4) -- (180:1.4) -- (270:1.4) -- cycle;
- \def\x{0.5}
- \fill[color=red!40,opacity=0.5]
- ({1.4*cosh(\x)},{1.4*sinh(\x})
- --
- ({1.4*sinh(\x},{1.4*cosh(\x)})
- --
- ({-1.4*cosh(\x)},{-1.4*sinh(\x})
- --
- ({-1.4*sinh(\x},{-1.4*cosh(\x)})
- -- cycle;
-
- \begin{scope}
- \clip (-2.1,-2.1) rectangle (2.2,2.2);
- \draw[color=darkgreen]
- plot[domain=-1:1,samples=100] ({1.4*cosh(\x)},{1.4*sinh(\x)});
- \draw[color=darkgreen]
- plot[domain=-1:1,samples=100] ({1.4*sinh(\x)},{1.4*cosh(\x)});
- \draw[color=darkgreen]
- plot[domain=-1:1,samples=100] ({-1.4*cosh(\x)},{1.4*sinh(\x)});
- \draw[color=darkgreen]
- plot[domain=-1:1,samples=100] ({1.4*sinh(\x)},{-1.4*cosh(\x)});
- \end{scope}
-
- \draw[->] (-2.1,0) -- (2.3,0) coordinate[label={$x$}];
- \draw[->] (0,-2.1) -- (0,2.3) coordinate[label={right:$y$}];
-
- \draw[->,color=blue] (0,0) -- (1.4,0);
- \draw[->,color=blue] (0,0) -- (0,1.4);
-
- \draw[->,color=red] (0,0) -- ({1.4*cosh(\x)},{1.4*sinh(\x)});
- \draw[->,color=red] (0,0) -- ({1.4*sinh(\x)},{1.4*cosh(\x)});
-
- \node at (0,-3.2) {$\displaystyle
- \begin{aligned}
- C&=\begin{pmatrix}0&1\\1&0\end{pmatrix}
- \\
- e^{Ct}
- &=
- \begin{pmatrix}
- \cosh t&\sinh t\\
- \sinh t&\cosh t
- \end{pmatrix}
- \end{aligned}
- $};
-\end{scope}
-
-\end{tikzpicture}
-\end{document}
-
+% +% sl2.tex -- template for standalon tikz images +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\begin{document} +\def\skala{1} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\definecolor{darkgreen}{rgb}{0,0.6,0} + +\begin{scope}[xshift=-4.5cm] + \fill[color=blue!20] + (1.4,0) -- (0,1.4) -- (-1.4,0) -- (0,-1.4) -- cycle; + \fill[color=red!40,opacity=0.5] + (1.96,0) -- (0,1) -- (-1.96,0) -- (0,-1) -- cycle; + + \begin{scope} + \clip (-2.1,-2.1) rectangle (2.3,2.3); + \draw[color=darkgreen] + plot[domain=-1:1,samples=100] + ({(1/1.4)*exp(\x)},{(1/1.4)*exp(-\x)}); + \draw[color=darkgreen] + plot[domain=-1:1,samples=100] + ({(1/1.4)*exp(\x)},{-(1/1.4)*exp(-\x)}); + \draw[color=darkgreen] + plot[domain=-1:1,samples=100] + ({-(1/1.4)*exp(\x)},{(1/1.4)*exp(-\x)}); + \draw[color=darkgreen] + plot[domain=-1:1,samples=100] + ({-(1/1.4)*exp(\x)},{-(1/1.4)*exp(-\x)}); + \end{scope} + + \draw[->] (-2.1,0) -- (2.3,0) coordinate[label={$x$}]; + \draw[->] (0,-2.1) -- (0,2.3) coordinate[label={right:$y$}]; + + \draw[->,color=blue] (0,0) -- (1.4,0); + \draw[->,color=blue] (0,0) -- (0,1.4); + + \draw[->,color=red] (0,0) -- (1.96,0); + \draw[->,color=red] (0,0) -- (0,1); + \node at (0,-3.2) + {$\displaystyle + \begin{aligned} + A&=\begin{pmatrix}1&0\\0&-1\end{pmatrix} + \\ + e^{At} + &=\begin{pmatrix}e^t&0\\0&e^{-t}\end{pmatrix} + \end{aligned} + $}; + +\end{scope} + + +\begin{scope} + \fill[color=blue!20] + (0:1.4) -- (90:1.4) -- (180:1.4) -- (270:1.4) -- cycle; + \fill[color=red!40,opacity=0.5] + (33:1.4) -- (123:1.4) -- (213:1.4) -- (303:1.4) -- cycle; + + \draw[color=darkgreen] (0,0) circle[radius=1.4]; + + \draw[->] (-2.1,0) -- (2.3,0) coordinate[label={$x$}]; + \draw[->] (0,-2.1) -- (0,2.3) coordinate[label={right:$y$}]; + + \draw[->,color=blue] (0,0) -- (1.4,0); + \draw[->,color=blue] (0,0) -- (0,1.4); + + \draw[->,color=red] (0,0) -- (33:1.4); + \draw[->,color=red] (0,0) -- (123:1.4); + + \node at (0,-3.2) + {$\displaystyle + \begin{aligned} + B + &=\begin{pmatrix}0&-1\\1&0 \end{pmatrix} + \\ + e^{Bt} + &= + \begin{pmatrix} + \cos t&-\sin t\\ + \sin t& \cos t + \end{pmatrix} + \end{aligned}$}; +\end{scope} + + +\begin{scope}[xshift=4.5cm] + \fill[color=blue!20] + (0:1.4) -- (90:1.4) -- (180:1.4) -- (270:1.4) -- cycle; + \def\x{0.5} + \fill[color=red!40,opacity=0.5] + ({1.4*cosh(\x)},{1.4*sinh(\x}) + -- + ({1.4*sinh(\x},{1.4*cosh(\x)}) + -- + ({-1.4*cosh(\x)},{-1.4*sinh(\x}) + -- + ({-1.4*sinh(\x},{-1.4*cosh(\x)}) + -- cycle; + + \begin{scope} + \clip (-2.1,-2.1) rectangle (2.2,2.2); + \draw[color=darkgreen] + plot[domain=-1:1,samples=100] ({1.4*cosh(\x)},{1.4*sinh(\x)}); + \draw[color=darkgreen] + plot[domain=-1:1,samples=100] ({1.4*sinh(\x)},{1.4*cosh(\x)}); + \draw[color=darkgreen] + plot[domain=-1:1,samples=100] ({-1.4*cosh(\x)},{1.4*sinh(\x)}); + \draw[color=darkgreen] + plot[domain=-1:1,samples=100] ({1.4*sinh(\x)},{-1.4*cosh(\x)}); + \end{scope} + + \draw[->] (-2.1,0) -- (2.3,0) coordinate[label={$x$}]; + \draw[->] (0,-2.1) -- (0,2.3) coordinate[label={right:$y$}]; + + \draw[->,color=blue] (0,0) -- (1.4,0); + \draw[->,color=blue] (0,0) -- (0,1.4); + + \draw[->,color=red] (0,0) -- ({1.4*cosh(\x)},{1.4*sinh(\x)}); + \draw[->,color=red] (0,0) -- ({1.4*sinh(\x)},{1.4*cosh(\x)}); + + \node at (0,-3.2) {$\displaystyle + \begin{aligned} + C&=\begin{pmatrix}0&1\\1&0\end{pmatrix} + \\ + e^{Ct} + &= + \begin{pmatrix} + \cosh t&\sinh t\\ + \sinh t&\cosh t + \end{pmatrix} + \end{aligned} + $}; +\end{scope} + +\end{tikzpicture} +\end{document} + |