From a866d7cd6672474e9376617aadc91424b9ba3506 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Sun, 8 May 2022 22:37:45 +0200
Subject: add Fresnel presentation

---
 vorlesungen/slides/fresnel/kruemmung.tex | 91 ++++++++++++++++++++++++++++++++
 1 file changed, 91 insertions(+)
 create mode 100644 vorlesungen/slides/fresnel/kruemmung.tex

(limited to 'vorlesungen/slides/fresnel/kruemmung.tex')

diff --git a/vorlesungen/slides/fresnel/kruemmung.tex b/vorlesungen/slides/fresnel/kruemmung.tex
new file mode 100644
index 0000000..e75611b
--- /dev/null
+++ b/vorlesungen/slides/fresnel/kruemmung.tex
@@ -0,0 +1,91 @@
+%
+% kruemmung.tex -- slide template
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\bgroup
+\begin{frame}[t]
+\setlength{\abovedisplayskip}{5pt}
+\setlength{\belowdisplayskip}{5pt}
+\frametitle{Krümmung einer Kurve}
+\vspace{-20pt}
+\begin{columns}[t,onlytextwidth]
+\begin{column}{0.48\textwidth}
+\begin{block}{Krümmungsradius}
+Bogen und Radius:
+\[
+s=r\cdot\Delta\varphi
+\uncover<2->{
+\quad
+\Rightarrow
+\quad
+r
+=
+\frac{s}{\Delta\varphi}
+}
+\]
+\end{block}
+\vspace*{-12pt}
+\uncover<3->{
+\begin{block}{Krümmung}
+Je grösser der Krümmungsradius, desto kleiner die Krümmung:
+\[
+\kappa = \frac{1}{r}
+\]
+\end{block}}
+\vspace*{-12pt}
+\uncover<5->{%
+\begin{block}{Definition}
+Änderungsgeschwindigkeit des Polarwinkels der Tangente
+\[
+\kappa
+=
+\frac{1}{r}
+\uncover<6->{=
+\frac{\Delta\varphi}{s}}
+\uncover<7->{=
+\frac{d\varphi}{dt}}
+\]
+\end{block}}
+\end{column}
+\begin{column}{0.48\textwidth}
+\begin{center}
+\begin{tikzpicture}[>=latex,thick]
+
+\begin{scope}
+\clip (-1,-1) rectangle (4,4);
+
+\def\r{3}
+\def\winkel{30}
+
+\fill[color=blue!20] (0,0) -- (0:\r) arc (0:\winkel:\r) -- cycle;
+\node[color=blue] at ({0.5*\winkel}:{0.5*\r}) {$\Delta\varphi$};
+
+\draw[line width=0.3pt] (0,0) circle[radius=\r];
+
+\draw[->] (0,0) -- (0:\r);
+\draw[->] (0,0) -- (\winkel:\r);
+
+\uncover<4->{
+\draw[->] (0:\r) -- ($(0:\r)+(90:0.7*\r)$);
+\draw[->] (\winkel:\r) -- ($(\winkel:\r)+({90+\winkel}:0.7*\r)$);
+}
+
+\draw[color=red,line width=1.4pt] (0:\r) arc (0:\winkel:\r);
+\node[color=red] at ({0.5*\winkel}:\r) [left] {$s$};
+\fill[color=red] (0:\r) circle[radius=0.05];
+\fill[color=red] (\winkel:\r) circle[radius=0.05];
+
+\node at (\winkel:{0.5*\r}) [above] {$r$};
+\node at (0:{0.5*\r}) [below] {$r$};
+\end{scope}
+
+\end{tikzpicture}
+\end{center}
+\uncover<4->{%
+Für $\varphi$ kann man auch den Polarwinkel des Tangentialvektors nehmen
+}
+\end{column}
+\end{columns}
+\end{frame}
+\egroup
-- 
cgit v1.2.1


From db0fcc225416e260284ffa3a1da5919a2b1ac5a5 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Mon, 9 May 2022 11:03:14 +0200
Subject: =?UTF-8?q?Fresnel-Pr=C3=A4sentation?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

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

(limited to 'vorlesungen/slides/fresnel/kruemmung.tex')

diff --git a/vorlesungen/slides/fresnel/kruemmung.tex b/vorlesungen/slides/fresnel/kruemmung.tex
index e75611b..06f6b9b 100644
--- a/vorlesungen/slides/fresnel/kruemmung.tex
+++ b/vorlesungen/slides/fresnel/kruemmung.tex
@@ -1,5 +1,5 @@
 %
-% kruemmung.tex -- slide template
+% kruemmung.tex -- Kruemmung
 %
 % (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
 %
-- 
cgit v1.2.1

