diff options
Diffstat (limited to 'info/examples/PSTricks_7_de/35-00-48.ltx')
-rw-r--r-- | info/examples/PSTricks_7_de/35-00-48.ltx | 187 |
1 files changed, 187 insertions, 0 deletions
diff --git a/info/examples/PSTricks_7_de/35-00-48.ltx b/info/examples/PSTricks_7_de/35-00-48.ltx new file mode 100644 index 0000000000..c6ed2826ac --- /dev/null +++ b/info/examples/PSTricks_7_de/35-00-48.ltx @@ -0,0 +1,187 @@ +%% +%% Ein Beispiel der DANTE-Edition +%% +%% 7. Auflage +%% +%% Beispiel 35-00-48 auf Seite 838. +%% +%% Copyright (C) 2016 Herbert Voss +%% +%% It may be distributed and/or modified under the conditions +%% of the LaTeX Project Public License, either version 1.3 +%% of this license or (at your option) any later version. +%% +%% See http://www.latex-project.org/lppl.txt for details. +%% +%% +%% ==== +% Show page(s) 1 +%% +%% +\documentclass[]{exaarticle} +\pagestyle{empty} +\setlength\textwidth{352.81416pt} +\setlength\parindent{0pt} +\usepackage[a3paper,landscape,dvips,margin=5mm]{geometry} +%StartShownPreambleCommands +\usepackage{pst-slpe,pstricks-add,graphicx} +\newpsstyle{magenta40}{fillstyle=solid,fillcolor=magenta!40} +\newpsstyle{blue40}{fillstyle=solid,fillcolor=blue!60} +\newpsstyle{Blackball}{fillstyle=ccslope,slopebegin=white,slopeend=black, + slopecenter={0.6 0.6}} +\newpsstyle{Blueball}{fillstyle=ccslope,slopebegin=white,slopeend=blue, + slopecenter={0.6 0.6}} +\newpsstyle{Redball}{fillstyle=ccslope,slopebegin=white,slopeend=red, + slopecenter={0.6 0.6}} +% inclined plane +\newcommand*\ChronoSlope{30 } +\newcommand*\ChronoSlopeN{180 \ChronoSlope sub } +% Length of inclined plane (that is, the ball course!) +\newcommand*\ChronoLength{15 } +\newcommand*\rBall{0.5 } +\makeatletter +\pst@dima=\rBall pt +\pst@dimb=0.5\pst@dima +\edef\rBallinner{\strip@pt\pst@dimb} +\makeatother +\newcommand*\mass{1 } +\def\Acceleration{9.81 \ChronoSlope sin mul } +\def\AccelerationRot{\Acceleration 5 mul 7 div } +\def\S#1{ % way as function of time, returns x y + 0.5 \Acceleration mul #1 dup mul mul % S(t) + dup \ChronoSlope cos mul % Sx + exch \ChronoSlope sin mul neg \CVL add } % Sy +\def\Srot#1{ % way as function of time, returns x y + 0.5 \AccelerationRot mul #1 dup mul mul % S(t) + dup \ChronoSlope cos mul % Sx + exch \ChronoSlope sin mul neg \CVL add } % Sy +\def\tEnd{2 \ChronoLength mul \Acceleration div sqrt } +\def\tEndRot{2 \ChronoLength mul \AccelerationRot div sqrt } +\newcommand*{\CHL}{\ChronoSlope cos \ChronoLength mul }% Chrono Horizontal Length +\newcommand*{\CVL}{\ChronoSlope sin \ChronoLength mul }% Chrono Vertical Length + +%StopShownPreambleCommands +\begin{document} +\begin{pspicture}(-1,-1)(15.5,10.5) + \pspolygon[style=magenta40](0,0)(!\CHL 0)(!0 \CVL)\psline(!\CHL 0)(!\CHL 2 add 0) + \rput[rt](13,8){\large\textbf{A gliding ball}} + \multido{\nt=0+0.25}{10}{% Chronophotography (one shot per 1/4 second) + \rput(! \S{\nt} ){% + \pscircle[style=Blackball](!90 \ChronoSlope sub cos \rBall mul + 90 \ChronoSlope sub sin \rBall mul){\rBall}} + \psline[linestyle=dashed]{*-}(! \S{\nt} )(! \S{\nt} pop -0.2) + }% end of multido + \rput(! \S{2.5} pop 0 ){\pscircle[style=Blackball](0,\rBall){\rBall}} + \psline[arrowscale=2]{->}(! \S{2.5} pop \rBall )(! \S{2.5} pop 1 add \rBall ) + \rput{-\ChronoSlope}(! \S{2.25} ){% + \psline[arrowscale=2]{->}(! 0 90 \ChronoSlope add sin \rBall mul) + (! 1 90 \ChronoSlope add sin \rBall mul)} + \psset{linewidth=0.2pt,tbarsize=5mm,arrowscale=2,arrows=|<->|} + \pcline(-0.75,0)(!-0.75 \CVL) \ncput*[nrot=:U]{length\,$\cdot\sin\alpha$} + \pcline(0,-0.75)(! \CHL -0.75) \ncput*{length\,$\cdot\cos\alpha$} + \rput{-\ChronoSlope}% + (!\rBall 4 mul \ChronoSlope sin mul + \CVL \rBall 4 mul \ChronoSlope cos mul add)% + {\pcline(0,0)(\ChronoLength,0)\ncput*{length=15\,m}} + \psarcn[arrows=<-](!\CHL 0){3}{180}{!\ChronoSlopeN} + \uput*{2cm}[165](!\CHL 0){$\alpha=30^\circ$} +\end{pspicture} +\quad +\begin{pspicture}(-1,-1)(15.5,10.5) + \pspolygon[style=magenta40](0,0)(!\CHL 0)(!0 \CVL)\psline(!\CHL 0)(!\CHL 2 add 0) + \rput[rt](13,8){\large\textbf{A rolling ball}} + \multido{\nt=0+0.25}{12}{% Chronophotography (one shot per 1/4 second) + \rput(! \Srot{\nt} ){% + \pscircle[style=Blueball](!90 \ChronoSlope sub cos \rBall mul + 90 \ChronoSlope sub sin \rBall mul){\rBall} + \psarcn{->}(!90 \ChronoSlope sub cos \rBall mul + 90 \ChronoSlope sub sin \rBall mul){\rBallinner}{180}{0}} + \psline[linestyle=dashed]{*-}(! \Srot{\nt} )(! \Srot{\nt} pop -0.2) + }% end of multido + \rput(! \Srot{3} pop 0 ){\pscircle[style=Blueball](0,\rBall){\rBall}} + \psarcn{->}(!\Srot{3} pop \rBall ){\rBallinner}{190}{10} + \psline[arrowscale=2]{->}(! \Srot{3} pop \rBall )(! \Srot{3} pop 1 add \rBall ) + \rput{-\ChronoSlope}(! \Srot{2.75} ){% + \psline[arrowscale=2]{->}(! 0 90 \ChronoSlope add sin \rBall mul) + (! 1 90 \ChronoSlope add sin \rBall mul)} + \psset{linewidth=0.2pt,tbarsize=5mm,arrowscale=2,arrows=|<->|} + \pcline(-0.75,0)(!-0.75 \CVL) \ncput*[nrot=:U]{length\,$\cdot\sin\alpha$} + \pcline(0,-0.75)(! \CHL -0.75) \ncput*{length\,$\cdot\cos\alpha$} + \rput{-\ChronoSlope}% + (!\rBall 4 mul \ChronoSlope sin mul + \CVL \rBall 4 mul \ChronoSlope cos mul add)% + {\pcline(0,0)(\ChronoLength,0)\ncput*{length=15\,m}} + \psarcn[arrows=<-](!\CHL 0){3}{180}{!\ChronoSlopeN} + \uput*{2cm}[165](!\CHL 0){$\alpha=30^\circ$} +\end{pspicture}%} + +\vspace{1.5cm} +\hspace*{2pt}% only for positioning on paper, otherwise not important +\psset{llx=-1,lly=-1,xAxisLabel={$t\mathrm{[sec]}$}, + yAxisLabel={$s\mathrm{[m]} \,/\, v\mathrm{[m/sec]}$}}% $ +\resizebox{14.1cm}{!}{% +\begin{psgraph}[Dy=2,Dx=0.25]{->}(0,0)(2.5,16){13.2cm}{8cm} + \psline[linecolor=blue!50,linewidth=2pt]% + (! 2 \ChronoLength mul \Acceleration div sqrt -0.2)% + (! 2 \ChronoLength mul \Acceleration div sqrt 0.2) + \psplot[linecolor=blue,linewidth=2pt]{0}{\tEnd}{% S(t) + 0.5 \Acceleration mul x dup mul mul } + \psline[linecolor=blue,linewidth=2pt]% + (! \tEnd 0.5 \Acceleration mul \tEnd dup mul mul )% + (! \tEnd 0.2 add 0.5 \Acceleration mul \tEnd dup mul mul % tEnd+dt S(tEnd) + \Acceleration \tEnd mul % vEnd + 0.2 mul % vEnd * dt + add ) + \rput[lb](0.5,14){\color{blue}$s(t)=\frac{1}{2}(\,g\cdot\sin\alpha)\cdot t^2$} + \psline[linecolor=blue,linewidth=0.5pt,linestyle=dashed]% + (0,\ChronoLength)(! \tEnd \ChronoLength)(!\tEnd 0) + \uput*{20pt}[90](! \tEnd 0){\textbf{$t_{End}$}} %$ +% + \psplot[linecolor=red,linewidth=2pt]{0}{\tEnd}{% Sy(t) + 0.5 \Acceleration mul x dup mul mul \ChronoSlope sin mul neg \CVL add} + \rput[lb](0.5,13){\color{red}$h(t)=Height-\frac{1}{2}(\,g\cdot\sin^2\alpha)\cdot t^2\sim W_{pot}$} + \psline[linecolor=red,linewidth=2pt](!\tEnd 0)(!\tEnd 0.05 add 0) +% + \psplot[linecolor=green,linewidth=2pt]{0}{\tEnd}{% Sx(t) + 0.5 \Acceleration mul x dup mul mul \ChronoSlope cos mul } + \rput[lb](0.5,12){\color{green}$w(t)=\frac{1}{2}(\,g\cdot\sin\alpha\cos\alpha)\cdot t^2$} + \psplot[linestyle=dashed,linecolor=magenta,linewidth=2pt]{0}{\tEnd}{ \Acceleration x mul } + \rput[lb](0.5,11){\color{magenta}$v(t)=g\cdot\sin\alpha\cdot t\sim \sqrt{W_{kin}}$} + \psline[linecolor=black!60,linestyle=dashed,linewidth=2pt]% + (!0 \Acceleration)(!\tEnd \Acceleration) + \rput[lb](0.5,10){\color{black!60}$a(t)=g\cdot\sin\alpha$} +\end{psgraph}} +\hspace{2.7cm} +\resizebox{14.3cm}{!}{% +\begin{psgraph}[Dy=2,Dx=0.25]{->}(0,0)(3,16){13.2cm}{8cm} + \psline[linecolor=blue!50,linewidth=2pt]% + (! 2 \ChronoLength mul \AccelerationRot div sqrt -0.2)% + (! 2 \ChronoLength mul \AccelerationRot div sqrt 0.2) + \psplot[linecolor=blue,linewidth=2pt]{0}{\tEndRot}{% S(t) + 0.5 \AccelerationRot mul x dup mul mul } + \psline[linecolor=blue,linewidth=2pt]% + (! \tEndRot 0.5 \AccelerationRot mul \tEndRot dup mul mul )% + (! \tEndRot 0.2 add 0.5 \AccelerationRot mul \tEndRot dup mul mul % tEnd+dt S(tEnd) + \AccelerationRot \tEndRot mul % vEnd + 0.2 mul % vEnd * dt + add ) + \rput[lb](0.5,14){\color{blue}$s(t)=\frac{5}{14}(\,g\cdot\sin\alpha)\cdot t^2$} + \psline[linecolor=blue,linewidth=0.5pt,linestyle=dashed]% + (0,\ChronoLength)(! \tEndRot \ChronoLength)(!\tEndRot 0) + \uput*{20pt}[90](! \tEndRot 0){\textbf{$t_{End}$}}% $ +% + \psplot[linecolor=red,linewidth=2pt]{0}{\tEndRot}{% Sy(t) + 0.5 \AccelerationRot mul x dup mul mul \ChronoSlope sin mul neg \CVL add} + \rput[lb](0.5,13){\color{red}$h(t)=Height-\frac{5}{14}(\,g\cdot\sin^2\alpha)\cdot t^2\sim W_{pot}$} + \psline[linecolor=red,linewidth=2pt](!\tEndRot 0)(!\tEndRot 0.05 add 0) +% + \psplot[linecolor=green,linewidth=2pt]{0}{\tEndRot}{% Sx(t) + 0.5 \AccelerationRot mul x dup mul mul \ChronoSlope cos mul } + \rput[lb](0.5,12){\color{green}$w(t)=\frac{5}{14}(\,g\cdot\sin\alpha\cos\alpha)\cdot t^2$} + \psplot[linestyle=dashed,linecolor=magenta,linewidth=2pt]{0}{\tEndRot}{ \AccelerationRot x mul } + \rput[lb](0.5,11){\color{magenta}$v(t)=\frac{5}{7}\cdot g\cdot\sin\alpha\cdot t\sim \sqrt{W_{kin}}$} + \psline[linecolor=black!60,linestyle=dashed,linewidth=2pt]% + (!0 \AccelerationRot)(!\tEndRot \AccelerationRot) + \rput[lb](0.5,10){\color{black!60}$a(t)=\frac{5}{7}\cdot g\cdot\sin\alpha$} +\end{psgraph}} +\end{document} |