From 2db90bfe4b174570424c408f04000902411d8755 Mon Sep 17 00:00:00 2001
From: Joshua Baer <the.baer.joshua@gmail.ch>
Date: Mon, 12 Apr 2021 21:51:55 +0200
Subject: update to current state of book

---
 vorlesungen/slides/7/parameter.tex | 214 ++++++++++++++++++-------------------
 1 file changed, 107 insertions(+), 107 deletions(-)

(limited to 'vorlesungen/slides/7/parameter.tex')

diff --git a/vorlesungen/slides/7/parameter.tex b/vorlesungen/slides/7/parameter.tex
index 52c8e4a..afc67c5 100644
--- a/vorlesungen/slides/7/parameter.tex
+++ b/vorlesungen/slides/7/parameter.tex
@@ -1,107 +1,107 @@
-%
-% parameter.tex -- Parametrisierung der Matrizen
-%
-% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
-%
-\bgroup
-\definecolor{darkgreen}{rgb}{0,0.6,0}
-\definecolor{darkyellow}{rgb}{1,0.8,0}
-\begin{frame}[t]
-\setlength{\abovedisplayskip}{5pt}
-\setlength{\belowdisplayskip}{5pt}
-\frametitle{Drehungen Parametrisieren}
-\vspace{-20pt}
-\begin{columns}[t,onlytextwidth]
-\begin{column}{0.4\textwidth}
-\begin{block}{Drehung um Achsen}
-\vspace{-12pt}
-\begin{align*}
-\uncover<2->{
-D_{x,\alpha}
-&=
-\begin{pmatrix}
-1&0&0\\0&\cos\alpha&-\sin\alpha\\0&\sin\alpha&\cos\alpha
-\end{pmatrix}
-}
-\\
-\uncover<3->{
-D_{y,\beta}
-&=
-\begin{pmatrix}
-\cos\beta&0&\sin\beta\\0&1&0\\-\sin\beta&0&\cos\beta
-\end{pmatrix}
-}
-\\
-\uncover<4->{
-D_{z,\gamma}
-&=
-\begin{pmatrix}
-\cos\gamma&-\sin\gamma&0\\\sin\gamma&\cos\gamma&0\\0&0&1
-\end{pmatrix}
-}
-\intertext{\uncover<5->{beliebige Drehung:}}
-\uncover<5->{
-D
-&=
-D_{x,\alpha}
-D_{y,\beta}
-D_{z,\gamma}
-}
-\end{align*}
-\end{block}
-\end{column}
-\begin{column}{0.56\textwidth}
-\uncover<6->{%
-\begin{block}{Drehung um $\vec{\omega}\in\mathbb{R}^3$: 3-dimensional}
-\uncover<7->{%
-$\omega=|\vec{\omega}|=\mathstrut$Drehwinkel
-}
-\\
-\uncover<8->{%
-$\vec{k}=\vec{\omega}^0=\mathstrut$Drehachse
-}
-\[
-\uncover<9->{
-{\color{red}\vec{x}}
-\mapsto
-}
-\uncover<10->{
-({\color{darkyellow}\vec{x} -(\vec{k}\cdot\vec{x})\vec{k}})
-\cos\omega
-+
-}
-\uncover<11->{
-({\color{darkgreen}\vec{x}\times\vec{k}}) \sin\omega
-+
-}
-\uncover<9->{
-{\color{blue}\vec{k}} (\vec{k}\cdot\vec{x}) 
-}
-\]
-\vspace{-40pt}
-\begin{center}
-\begin{tikzpicture}[>=latex,thick]
-\uncover<9->{
-	\node at (0,0)
-		{\includegraphics[width=\textwidth]{../slides/7/images/rodriguez.jpg}};
-	\node[color=red] at (1.6,-0.9) {$\vec{x}$};
-	\node[color=blue] at (0.5,2) {$\vec{k}$};
-}
-\uncover<11->{
-	\node[color=darkgreen] at (-3,1.1) {$\vec{x}\times\vec{k}$};
-}
-\uncover<10->{
-	\node[color=yellow] at (2.2,-0.2)
-		{$\vec{x}-(\vec{x}\cdot\vec{k})\vec{k}$};
-}
-\end{tikzpicture}
-\end{center}
-\end{block}}
-\end{column}
-\end{columns}
-\vspace{-15pt}
-\uncover<5->{%
-{\usebeamercolor[fg]{title}Dimension:} $\operatorname{SO}(3)$ ist eine
-dreidimensionale Gruppe}
-\end{frame}
-\egroup
+%
+% parameter.tex -- Parametrisierung der Matrizen
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\bgroup
+\definecolor{darkgreen}{rgb}{0,0.6,0}
+\definecolor{darkyellow}{rgb}{1,0.8,0}
+\begin{frame}[t]
+\setlength{\abovedisplayskip}{5pt}
+\setlength{\belowdisplayskip}{5pt}
+\frametitle{Drehungen Parametrisieren}
+\vspace{-20pt}
+\begin{columns}[t,onlytextwidth]
+\begin{column}{0.4\textwidth}
+\begin{block}{Drehung um Achsen}
+\vspace{-12pt}
+\begin{align*}
+\uncover<2->{
+D_{x,\alpha}
+&=
+\begin{pmatrix}
+1&0&0\\0&\cos\alpha&-\sin\alpha\\0&\sin\alpha&\cos\alpha
+\end{pmatrix}
+}
+\\
+\uncover<3->{
+D_{y,\beta}
+&=
+\begin{pmatrix}
+\cos\beta&0&\sin\beta\\0&1&0\\-\sin\beta&0&\cos\beta
+\end{pmatrix}
+}
+\\
+\uncover<4->{
+D_{z,\gamma}
+&=
+\begin{pmatrix}
+\cos\gamma&-\sin\gamma&0\\\sin\gamma&\cos\gamma&0\\0&0&1
+\end{pmatrix}
+}
+\intertext{\uncover<5->{beliebige Drehung:}}
+\uncover<5->{
+D
+&=
+D_{x,\alpha}
+D_{y,\beta}
+D_{z,\gamma}
+}
+\end{align*}
+\end{block}
+\end{column}
+\begin{column}{0.56\textwidth}
+\uncover<6->{%
+\begin{block}{Drehung um $\vec{\omega}\in\mathbb{R}^3$: 3-dimensional}
+\uncover<7->{%
+$\omega=|\vec{\omega}|=\mathstrut$Drehwinkel
+}
+\\
+\uncover<8->{%
+$\vec{k}=\vec{\omega}^0=\mathstrut$Drehachse
+}
+\[
+\uncover<9->{
+{\color{red}\vec{x}}
+\mapsto
+}
+\uncover<10->{
+({\color{darkyellow}\vec{x} -(\vec{k}\cdot\vec{x})\vec{k}})
+\cos\omega
++
+}
+\uncover<11->{
+({\color{darkgreen}\vec{x}\times\vec{k}}) \sin\omega
++
+}
+\uncover<9->{
+{\color{blue}\vec{k}} (\vec{k}\cdot\vec{x}) 
+}
+\]
+\vspace{-40pt}
+\begin{center}
+\begin{tikzpicture}[>=latex,thick]
+\uncover<9->{
+	\node at (0,0)
+		{\includegraphics[width=\textwidth]{../slides/7/images/rodriguez.jpg}};
+	\node[color=red] at (1.6,-0.9) {$\vec{x}$};
+	\node[color=blue] at (0.5,2) {$\vec{k}$};
+}
+\uncover<11->{
+	\node[color=darkgreen] at (-3,1.1) {$\vec{x}\times\vec{k}$};
+}
+\uncover<10->{
+	\node[color=yellow] at (2.2,-0.2)
+		{$\vec{x}-(\vec{x}\cdot\vec{k})\vec{k}$};
+}
+\end{tikzpicture}
+\end{center}
+\end{block}}
+\end{column}
+\end{columns}
+\vspace{-15pt}
+\uncover<5->{%
+{\usebeamercolor[fg]{title}Dimension:} $\operatorname{SO}(3)$ ist eine
+dreidimensionale Gruppe}
+\end{frame}
+\egroup
-- 
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