From 1fb743df08b0734932d510c6b11405d0a2dbbe47 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Sat, 10 Apr 2021 19:57:13 +0200
Subject: new slides

---
 vorlesungen/slides/7/parameter.tex | 58 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 58 insertions(+)
 create mode 100644 vorlesungen/slides/7/parameter.tex

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

diff --git a/vorlesungen/slides/7/parameter.tex b/vorlesungen/slides/7/parameter.tex
new file mode 100644
index 0000000..ec129bb
--- /dev/null
+++ b/vorlesungen/slides/7/parameter.tex
@@ -0,0 +1,58 @@
+%
+% parameter.tex -- Parametrisierung der Matrizen
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\bgroup
+\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}
+\begin{align*}
+D_{x,\alpha}
+&=
+\begin{pmatrix}
+1&0&0\\0&\cos\alpha&-\sin\alpha\\0&\sin\alpha&\cos\alpha
+\end{pmatrix}
+\\
+D_{y,\beta}
+&=
+\begin{pmatrix}
+\cos\beta&0&-\sin\beta\\0&1&0\\\sin\beta&0&\cos\beta
+\end{pmatrix}
+\\
+D_{z,\gamma}
+&=
+\begin{pmatrix}
+\cos\gamma&-\sin\gamma&0\\\sin\gamma&\cos\gamma&0\\0&0&1
+\end{pmatrix}
+\end{align*}
+\end{block}
+\end{column}
+\begin{column}{0.56\textwidth}
+\begin{block}{Drehung um $\vec{\omega}$}
+$\omega=|\vec{\omega}|=\mathstrut$Drehwinkel
+\\
+$\vec{k}=\vec{\omega}^0=\mathstrut$Drehachse
+\[
+\vec{x}
+\mapsto
+\cos\omega
+\vec{x}
++
+(\vec{k}\times\vec{x})\sin\omega
++
+\vec{k}(\vec{k}\cdot\vec{x}) (1-\cos\omega)
+\]
+XXX TODO: Bild für Rodriguez Formel
+\end{block}
+\end{column}
+\end{columns}
+{\usebeamercolor[fg]{title}Dimension:} $\operatorname{SO}(3)$ ist eine
+dreidimensionale Gruppe
+\end{frame}
+\egroup
-- 
cgit v1.2.1


From 7242d266e3e348e40209ac51e703a0acb6d78ca3 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Sat, 10 Apr 2021 21:13:29 +0200
Subject: add rodriguez image

---
 vorlesungen/slides/7/parameter.tex | 17 ++++++++++++++---
 1 file changed, 14 insertions(+), 3 deletions(-)

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

diff --git a/vorlesungen/slides/7/parameter.tex b/vorlesungen/slides/7/parameter.tex
index ec129bb..b719207 100644
--- a/vorlesungen/slides/7/parameter.tex
+++ b/vorlesungen/slides/7/parameter.tex
@@ -4,6 +4,7 @@
 % (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
 %
 \bgroup
+\definecolor{darkgreen}{rgb}{0,0.6,0}
 \begin{frame}[t]
 \setlength{\abovedisplayskip}{5pt}
 \setlength{\belowdisplayskip}{5pt}
@@ -41,17 +42,27 @@ $\vec{k}=\vec{\omega}^0=\mathstrut$Drehachse
 \[
 \vec{x}
 \mapsto
+(\vec{x} -(\vec{k}\cdot\vec{x})\vec{k})
 \cos\omega
-\vec{x}
 +
 (\vec{k}\times\vec{x})\sin\omega
 +
-\vec{k}(\vec{k}\cdot\vec{x}) (1-\cos\omega)
+\vec{k}(\vec{k}\cdot\vec{x}) 
 \]
-XXX TODO: Bild für Rodriguez Formel
+\vspace{-40pt}
+\begin{center}
+\begin{tikzpicture}[>=latex,thick]
+\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) {$\vec{x}-(\vec{x}\cdot\vec{k})\vec{k}$};
+\end{tikzpicture}
+\end{center}
 \end{block}
 \end{column}
 \end{columns}
+\vspace{-15pt}
 {\usebeamercolor[fg]{title}Dimension:} $\operatorname{SO}(3)$ ist eine
 dreidimensionale Gruppe
 \end{frame}
-- 
cgit v1.2.1


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}
-- 
cgit v1.2.1


From 78a4379a40a594fd89a74bbb0d5e6cc52f8213f6 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Sun, 11 Apr 2021 11:03:04 +0200
Subject: typos

---
 vorlesungen/slides/7/parameter.tex | 15 ++++++++++-----
 1 file changed, 10 insertions(+), 5 deletions(-)

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

diff --git a/vorlesungen/slides/7/parameter.tex b/vorlesungen/slides/7/parameter.tex
index 1e8549c..12b5221 100644
--- a/vorlesungen/slides/7/parameter.tex
+++ b/vorlesungen/slides/7/parameter.tex
@@ -61,8 +61,10 @@ $\omega=|\vec{\omega}|=\mathstrut$Drehwinkel
 $\vec{k}=\vec{\omega}^0=\mathstrut$Drehachse
 }
 \[
+\uncover<9->{
 {\color{red}\vec{x}}
 \mapsto
+}
 \uncover<10->{
 ({\color{darkyellow}\vec{x} -(\vec{k}\cdot\vec{x})\vec{k}})
 \cos\omega
@@ -79,10 +81,12 @@ $\vec{k}=\vec{\omega}^0=\mathstrut$Drehachse
 \vspace{-40pt}
 \begin{center}
 \begin{tikzpicture}[>=latex,thick]
-\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<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) {$\vec{x}\times\vec{k}$};
 }
@@ -96,7 +100,8 @@ $\vec{k}=\vec{\omega}^0=\mathstrut$Drehachse
 \end{column}
 \end{columns}
 \vspace{-15pt}
+\uncover<5->{%
 {\usebeamercolor[fg]{title}Dimension:} $\operatorname{SO}(3)$ ist eine
-dreidimensionale Gruppe
+dreidimensionale Gruppe}
 \end{frame}
 \egroup
-- 
cgit v1.2.1


From 2a2f981422ab9c2ab11c69c19b87ffda6d0f855a Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Mon, 12 Apr 2021 14:03:27 +0200
Subject: typo

---
 vorlesungen/slides/7/parameter.tex | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

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

diff --git a/vorlesungen/slides/7/parameter.tex b/vorlesungen/slides/7/parameter.tex
index 12b5221..52c8e4a 100644
--- a/vorlesungen/slides/7/parameter.tex
+++ b/vorlesungen/slides/7/parameter.tex
@@ -28,7 +28,7 @@ D_{x,\alpha}
 D_{y,\beta}
 &=
 \begin{pmatrix}
-\cos\beta&0&-\sin\beta\\0&1&0\\\sin\beta&0&\cos\beta
+\cos\beta&0&\sin\beta\\0&1&0\\-\sin\beta&0&\cos\beta
 \end{pmatrix}
 }
 \\
-- 
cgit v1.2.1


From 3fe0e1a234175903de4a161444b9db9810956f9d Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Thu, 29 Apr 2021 09:03:37 +0200
Subject: add new slides

---
 vorlesungen/slides/7/parameter.tex | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

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

diff --git a/vorlesungen/slides/7/parameter.tex b/vorlesungen/slides/7/parameter.tex
index 52c8e4a..f3579a3 100644
--- a/vorlesungen/slides/7/parameter.tex
+++ b/vorlesungen/slides/7/parameter.tex
@@ -14,7 +14,7 @@
 \begin{columns}[t,onlytextwidth]
 \begin{column}{0.4\textwidth}
 \begin{block}{Drehung um Achsen}
-\vspace{-12pt}
+%\vspace{-12pt}
 \begin{align*}
 \uncover<2->{
 D_{x,\alpha}
-- 
cgit v1.2.1

