diff options
Diffstat (limited to 'buch/chapters/110-elliptisch/images')
| -rw-r--r-- | buch/chapters/110-elliptisch/images/Makefile | 5 | ||||
| -rw-r--r-- | buch/chapters/110-elliptisch/images/ellipse.pdf | bin | 0 -> 17658 bytes | |||
| -rw-r--r-- | buch/chapters/110-elliptisch/images/ellipse.tex | 78 |
3 files changed, 82 insertions, 1 deletions
diff --git a/buch/chapters/110-elliptisch/images/Makefile b/buch/chapters/110-elliptisch/images/Makefile index ef2e6fc..afa70ba 100644 --- a/buch/chapters/110-elliptisch/images/Makefile +++ b/buch/chapters/110-elliptisch/images/Makefile @@ -3,8 +3,11 @@ # # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # -all: lemniskate.pdf +all: lemniskate.pdf ellipse.pdf lemniskate.pdf: lemniskate.tex pdflatex lemniskate.tex +ellipse.pdf: ellipse.tex + pdflatex ellipse.tex + diff --git a/buch/chapters/110-elliptisch/images/ellipse.pdf b/buch/chapters/110-elliptisch/images/ellipse.pdf Binary files differnew file mode 100644 index 0000000..9cdd2a1 --- /dev/null +++ b/buch/chapters/110-elliptisch/images/ellipse.pdf diff --git a/buch/chapters/110-elliptisch/images/ellipse.tex b/buch/chapters/110-elliptisch/images/ellipse.tex new file mode 100644 index 0000000..f6f1344 --- /dev/null +++ b/buch/chapters/110-elliptisch/images/ellipse.tex @@ -0,0 +1,78 @@ +% +% ellipse.tex -- Abbildung der Ellipsen zur Herleitung der Jacobi +% elliptischen Funktionen +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math,calc} +\begin{document} +\def\skala{0.72} +\begin{tikzpicture}[>=latex,thick,scale=\skala] +\definecolor{darkgreen}{rgb}{0,0.6,0} + +% add image content here +\def\winkel{70} +\def\a{5} +\def\b{3} +\pgfmathparse{sqrt(\a*\a-\b*\b)} +\xdef\e{\pgfmathresult} + +\fill[color=gray!20] (0,0) -- plot[domain=0:\winkel,samples=100] + ({5*cos(\x)},{3*sin(\x)}) + -- cycle; +\draw (0,0) -- ({5*cos(\winkel)},{3*sin(\winkel)}); +\draw[color=red,line width=1.4pt] plot[domain=0:\winkel,samples=100] + ({5*cos(\x)},{3*sin(\x)}); +\node at (5,0) [below right] {$a$}; +\node at (0,3) [above left] {$b$}; +\fill[color=red] ({5*cos(\winkel)},{3*sin(\winkel)}) circle[radius=0.08]; +\draw[color=red,line width=1pt] (0,0) ellipse (5cm and 3cm); +%\node at ({5*cos(\winkel/2)},{3*sin(\winkel/2)}) [above right] {$u$}; + +\node at ({5*cos(\winkel)},{3*sin(\winkel)}) [above right] {$P=(x,y)$}; + +\draw[->] (-5.2,0) -- (5.8,0);% coordinate[label={$x$}]; +\draw[->] (0,-3.2) -- (0,3.8);% coordinate[label={right:$y$}]; + +\draw[color=darkgreen] (0,0) -- (\e,0); +\draw[color=darkgreen] (0,0) -- (-\e,0); +\node[color=darkgreen] at ({0.5*\e},0) [below] {$e$}; +\node[color=darkgreen] at ({-0.5*\e},0) [below] {$-e$}; + + +\fill[color=blue] ({-\e},0) circle[radius=0.08]; +\node[color=blue] at (-\e,0) [below] {$F_1$}; +\fill[color=blue] ({\e},0) circle[radius=0.08]; +\node[color=blue] at (\e,0) [below] {$F_2$}; + +\draw[color=blue] (0,3) -- (\e,0); +\draw[color=blue] (0,3) -- (-\e,0); +\node[color=blue] at ($0.5*(0,3)+0.5*(\e,0)$) [below left] {$a$}; +\node[color=blue] at ($0.5*(0,3)+0.5*(-\e,0)$) [below right] {$a$}; +\fill[color=red] (0,3) circle[radius=0.08]; + +\node at (0,0) [below left] {$O$}; + +\begin{scope}[xshift=-9.5cm] +\fill[color=gray!20] (0,0) -- (3,0) arc (0:70:3) -- cycle; +\node[color=red] at (35:3) [above right] {$\varphi$}; +\draw (0,0) -- (70:3); +\node at (70:1.7) [left] {$r$}; +\draw[->] (-3.2,0) -- (3.8,0);% coordinate[label={$x$}]; +\draw[->] (0,-3.2) -- (0,3.8);% coordinate[label={right:$y$}]; +\draw[color=red,line width=1pt] (0,0) circle[radius=3]; +\draw[color=red,line width=1.4pt] (3,0) arc (0:70:3); +\fill[color=red] (70:3) circle[radius=0.08]; +\node at (70:3) [above right] {$P=(x,y)$}; +\node at (0,0) [below left] {$O$}; +\end{scope} + +\end{tikzpicture} +\end{document} + |