From 15881729aa3f1293d546a1692a02094ed3f24e2b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Sun, 11 Apr 2021 10:30:05 +0200
Subject: phases

---
 vorlesungen/slides/7/parameter.tex | 51 +++++++++++++++++++++++++++++++-------
 1 file changed, 42 insertions(+), 9 deletions(-)

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

diff --git a/vorlesungen/slides/7/parameter.tex b/vorlesungen/slides/7/parameter.tex
index b719207..1e8549c 100644
--- a/vorlesungen/slides/7/parameter.tex
+++ b/vorlesungen/slides/7/parameter.tex
@@ -5,6 +5,7 @@
 %
 \bgroup
 \definecolor{darkgreen}{rgb}{0,0.6,0}
+\definecolor{darkyellow}{rgb}{1,0.8,0}
 \begin{frame}[t]
 \setlength{\abovedisplayskip}{5pt}
 \setlength{\belowdisplayskip}{5pt}
@@ -13,53 +14,85 @@
 \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}
-\begin{block}{Drehung um $\vec{\omega}$}
+\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
+}
 \[
-\vec{x}
+{\color{red}\vec{x}}
 \mapsto
-(\vec{x} -(\vec{k}\cdot\vec{x})\vec{k})
+\uncover<10->{
+({\color{darkyellow}\vec{x} -(\vec{k}\cdot\vec{x})\vec{k}})
 \cos\omega
 +
-(\vec{k}\times\vec{x})\sin\omega
+}
+\uncover<11->{
+({\color{darkgreen}\vec{x}\times\vec{k}}) \sin\omega
 +
-\vec{k}(\vec{k}\cdot\vec{x}) 
+}
+\uncover<9->{
+{\color{blue}\vec{k}} (\vec{k}\cdot\vec{x}) 
+}
 \]
 \vspace{-40pt}
 \begin{center}
 \begin{tikzpicture}[>=latex,thick]
-\node at (0,0) {\includegraphics[width=\textwidth]{../slides/7/images/rodriguez.jpg}};
+\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) {$\vec{k}$};
-\node[color=darkgreen] at (-3,1.1) {$\vec{k}\times\vec{x}$};
-\node[color=yellow] at (2.2,-0.2) {$\vec{x}-(\vec{x}\cdot\vec{k})\vec{k}$};
+\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{block}}
 \end{column}
 \end{columns}
 \vspace{-15pt}
-- 
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