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authorKarl Berry <karl@freefriends.org>2006-01-09 00:56:57 +0000
committerKarl Berry <karl@freefriends.org>2006-01-09 00:56:57 +0000
commitf07bb53970ee2ecc53f81a206a3d3a67ef665e4a (patch)
tree6f57a1d62971db79e5ff023bdfd83b22cb971dc9 /Master/texmf-dist/doc/generic/pst-3dplot/examples/polar2.tex
parent007f67a693e4d031fd3d792df8e4d5f43e2cb2e7 (diff)
doc 6
git-svn-id: svn://tug.org/texlive/trunk@85 c570f23f-e606-0410-a88d-b1316a301751
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+\listfiles
+\documentclass[a4paper]{article}% Herbert Voss 2004-10-06
+\usepackage{pstricks}
+\usepackage{pstricks-add}
+\usepackage{multido}
+\def\func{%
+ const0 x sin dup mul 3 mul div neg /p exch def
+ p abs sqrt neg /r exch def
+ const1 2.0 div neg /q exch def
+ p 0 lt {
+ p dup mul p mul q dup mul add 0 le {
+ q r 3 exp div arccos
+ 3 div cos r dup add neg mul
+ }{
+ q r 3 exp div arch
+ 3 div cosh r dup add neg mul
+ } ifelse
+ }{
+ q r 3 exp div arsh
+ 3 div sinh r dup add neg mul
+ } ifelse
+}
+\begin{document}
+\textbf{Dynamical flow around a cylinder}
+\[
+\left(r^2-\frac{c_1}{r}\right)\sin^2\theta=c_0
+\]
+
+which is the same as
+
+\[
+r^3-\frac{c_0}{\sin^2\theta}\cdot r-c_1=0
+\]
+
+which can be solved by the formula of Cardano:
+
+\[
+r^3+3pr+2q=0
+\]
+
+\bigskip
+\begin{pspicture*}(-5,-2.5)(5,2.5)
+ \pstVerb{
+ /e 2.718281828459045 def
+ /arccos { dup dup mul neg 1.0 add sqrt exch atan } def
+ /sinh { dup e exch exp exch neg e exch exp sub 2 div } def
+ /cosh { dup e exch exp exch neg e exch exp add 2 div } def
+ /arsh { dup dup mul 1 add sqrt add ln } def
+ /arch { dup dup mul 1 sub sqrt add ln } def
+ }
+ \psaxes(0,0)(-5,-2.5)(5,2.5)
+ \pscircle[linecolor=red]{1}
+ \psset{plotpoints=100,linewidth=0.05pt,polarplot=true,linecolor=blue}
+ \multido{\rA=0.005+0.05}{5}{
+ \psplot{1}{179}{%
+ /const0 \rA\space def
+ /const1 1.0 def % cylinder radius
+ \func
+ }
+ \psplot{181}{359}{%
+ /const0 \rA\space def
+ /const1 1.0 def % cylinder radius
+ \func
+ }%
+ }
+ \multido{\rA=0.03+0.25}{20}{
+ \psplot{1}{179}{%
+ /const0 \rA\space def
+ /const1 1.0 def % cylinder radius
+ \func
+ }
+ \psplot{181}{359}{%
+ /const0 \rA\space def
+ /const1 1.0 def % cylinder radius
+ \func
+ }%
+ }
+\end{pspicture*}
+
+\end{document}
+