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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}
-