From 1fb743df08b0734932d510c6b11405d0a2dbbe47 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= 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?= 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?= 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?= 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?= 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?= 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