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authorKarl Berry <karl@freefriends.org>2021-12-29 21:33:34 +0000
committerKarl Berry <karl@freefriends.org>2021-12-29 21:33:34 +0000
commit7111273fb3a25b47f0bd582dc9872833d7f692c9 (patch)
tree608a2018eaaefe22ca6c32e2ba3ec956650c4ab3 /Master/texmf-dist/doc/generic/pst-vehicle
parentc165de88c35d5d85b2b90f4e9dff8ca516311a28 (diff)
pst-vehicle (29dec21)
git-svn-id: svn://tug.org/texlive/trunk@61438 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/generic/pst-vehicle')
-rw-r--r--Master/texmf-dist/doc/generic/pst-vehicle/Changes11
-rw-r--r--Master/texmf-dist/doc/generic/pst-vehicle/Changes.txt13
-rw-r--r--Master/texmf-dist/doc/generic/pst-vehicle/README.md36
-rw-r--r--Master/texmf-dist/doc/generic/pst-vehicle/pst-vehicle-doc-fr.pdfbin1877539 -> 1905668 bytes
-rw-r--r--Master/texmf-dist/doc/generic/pst-vehicle/pst-vehicle-doc-fr.tex49
-rw-r--r--Master/texmf-dist/doc/generic/pst-vehicle/pst-vehicle-doc.pdfbin1248734 -> 1903926 bytes
-rw-r--r--Master/texmf-dist/doc/generic/pst-vehicle/pst-vehicle-doc.tex227
7 files changed, 182 insertions, 154 deletions
diff --git a/Master/texmf-dist/doc/generic/pst-vehicle/Changes b/Master/texmf-dist/doc/generic/pst-vehicle/Changes
new file mode 100644
index 00000000000..3fbe8386739
--- /dev/null
+++ b/Master/texmf-dist/doc/generic/pst-vehicle/Changes
@@ -0,0 +1,11 @@
+pst-vehicle.tex ----------------
+
+1.3 2021/12/29 - fixes for running with lualatex (hv)
+ - fix for local use of variables x0->X0 (hv)
+1.2 2017/09/16 - node that can be called by name GravC, by default near
+ center of gravity that can become other coordinates
+1.1b 2017/06/23 - file ListVehicle to the right folder
+1.1a 2017/06/15 - add missing ListVehicle.tex
+1.1 2017/06/05 - fix for constant functions
+ - add option startPos to have a defined startrotation for the rear-wheel
+ - synchron start-rotation-position for front- and rear-wheel
diff --git a/Master/texmf-dist/doc/generic/pst-vehicle/Changes.txt b/Master/texmf-dist/doc/generic/pst-vehicle/Changes.txt
deleted file mode 100644
index 9c2ee14dee3..00000000000
--- a/Master/texmf-dist/doc/generic/pst-vehicle/Changes.txt
+++ /dev/null
@@ -1,13 +0,0 @@
-pst-vehicle.tex ----------------
-
-1.2 2017/09/16
-- node that can be called by name GravC, by default near
- center of gravity that can become other coordinates
-1.1b 2017/06/23
-- file ListVehicle to the right folder
-1.1a 2017/06/15
-- add missing ListVehicle.tex
-1.1 2017/06/05
-- fix for constant functions
-- add option startPos to have a defined startrotation for the rear-wheel
-- synchron start-rotation-position for front- and rear-wheel
diff --git a/Master/texmf-dist/doc/generic/pst-vehicle/README.md b/Master/texmf-dist/doc/generic/pst-vehicle/README.md
index b2020233db7..04bf8fe1f96 100644
--- a/Master/texmf-dist/doc/generic/pst-vehicle/README.md
+++ b/Master/texmf-dist/doc/generic/pst-vehicle/README.md
@@ -1,11 +1,33 @@
-The pst-vehicle package Author: J. Gilg, M. Luque, T. Söll
+# pst-vehicle: creating vehicles for physical animations
-Dated: 2017/09/16 Version 1.2
+This package was created to illustrate the notion of slope, the coefficient
+of the tangent line at a point of a curve. On the road, a rampant way or a
+dangerous descent due to their slope is indicated by a sign showing the
+percentage of the slope of this section of road, for example 10%.
-pst-vehicle contains the following:
+It was therefore quite obvious that the idea of representing a vehicle rolling
+without slipping on a curve came into our minds. Different types of vehicles
+are proposed, the shape of the curve is to be defined by its equation: $y=f(x)$
+in algebraic notation.
-1) pst-vehicle.sty
-2) pst-vehicle.tex
-3) ListVehicles.tex (in the same folder as pst-vehicle.tex)
+Save the files pst-vehicle.sty|data|tex in a directory, which is part of your
+local TeX tree. The pro file should go into $TEXMF/dvips/pstricks/
+Then do not forget to run texhash to update this tree.
-T. Söll
+pst-vehicle needs pstricks, which should be part of your local TeX installation,
+otherwise get it from a CTAN server, https://mirror.ctan.org
+
+PSTricks is PostScript Tricks, the documentation cannot be run
+with pdftex, use the sequence latex->dvips->ps2pdf or
+pdflatex with package auto-pst-pdf or xelatex or (best) lualatex
+
+This program can redistributed and/or modified under %%
+the terms of the LaTeX Project Public License %%
+Distributed from CTAN archives in directory %%
+macros/latex/base/lppl.txt; either version 1.3c of %%
+the License, or (at your option) any later version. %%
+
+Thomas Söll
+Bugs: hvoss@tug.org
+
+%% $Id: README.md 819 2018-09-26 06:40:48Z herbert $
diff --git a/Master/texmf-dist/doc/generic/pst-vehicle/pst-vehicle-doc-fr.pdf b/Master/texmf-dist/doc/generic/pst-vehicle/pst-vehicle-doc-fr.pdf
index 71c3c513b99..06cfea8d83b 100644
--- a/Master/texmf-dist/doc/generic/pst-vehicle/pst-vehicle-doc-fr.pdf
+++ b/Master/texmf-dist/doc/generic/pst-vehicle/pst-vehicle-doc-fr.pdf
Binary files differ
diff --git a/Master/texmf-dist/doc/generic/pst-vehicle/pst-vehicle-doc-fr.tex b/Master/texmf-dist/doc/generic/pst-vehicle/pst-vehicle-doc-fr.tex
index 44aa52ea56a..df6064298a7 100644
--- a/Master/texmf-dist/doc/generic/pst-vehicle/pst-vehicle-doc-fr.tex
+++ b/Master/texmf-dist/doc/generic/pst-vehicle/pst-vehicle-doc-fr.tex
@@ -1,22 +1,17 @@
-%% $Id: pst-pers-doc.tex 2017-04-05 Jürgen, Thomas $
-\documentclass[11pt,english,BCOR10mm,DIV12,bibliography=totoc,parskip=false,fleqn,
- smallheadings, headexclude,footexclude,oneside,dvipsnames,svgnames,x11names]{pst-doc}
-%\documentclass[11pt,english,BCOR10mm,DIV12,bibliography=totoc,parskip=false,smallheadings
-% headexclude,footexclude,oneside,dvipsnames,svgnames,distiller]{pst-doc}
-\usepackage[utf8]{inputenc}
+%% $Id: pst-vehicle-doc-fr.tex 376 2021-12-29 12:28:42Z herbert $
+\RequirePackage{pdfmanagement-testphase}
+\DeclareDocumentMetadata{}
+%
+\documentclass[11pt,english,BCOR=10mm,DIV=12,bibliography=totoc,parskip=false,headings=small,
+ headinclude=false,footinclude=false,oneside]{pst-doc}
\listfiles
\usepackage[autostyle]{csquotes}
\usepackage{biblatex}%\usepackage[style=dtk]{biblatex}
\addbibresource{pst-vehicle-doc.bib}
-\usepackage[utf8]{inputenc}
%\let\pstpersFV\fileversion
\usepackage[e]{esvect} % für schönere Vektorpfeile
\usepackage{pst-vehicle,pst-eucl,pstricks-add,animate}
\let\belowcaptionskip\abovecaptionskip
-
-\usepackage{etex} % um die Anzahl der Register zu erhöhen (sonst nur 256)
-
-
\newcommand{\qrq}{\ensuremath{\quad \Rightarrow \quad}}
\newcommand{\envert}[1]{\left\lvert#1\right\rvert}
\let\abs=\envert
@@ -94,15 +89,16 @@
\begin{document}
-\title{pst-vehicle v 1.0}
+\title{pst-vehicle v 1.3}
%\subtitle{A PSTricks package for slipping/rolling vehicles on curves of any kind of mathematical functions}
\subtitle{Un package PSTricks pour faire rouler sans glisser des véhicules sur des courbes définies par une fonction mathématique}
\author{Thomas \textsc{Söll}\\
avec la collaboration de\\
-Jürgen \textsc{Gilg} et Manuel \textsc{Luque}}
+Jürgen \textsc{Gilg} et Manuel \textsc{Luque}\\
+Herbert Voß (bugfixes)}
\date{\today}
-\maketitle
+\settitle
\tableofcontents
\psset{unit=1cm}
@@ -123,7 +119,7 @@ Il est également possible de dessiner son propre véhicule.
\end{abstract}
\clearpage
-\section{\protectÉtude théorique du roulement sans glissement, d'une roue sur une courbe}
+\section{Étude théorique du roulement sans glissement, d'une roue sur une courbe}
Dans cette première partie, nous établissons les résultats nécessaires permettant de déterminer suivant la position choisie pour le véhicule sur la courbe (l'abscisse du point de contact de roue arrière), les éléments suivants :
\begin{itemize}
\item la position du point de contact de la roue avant ;
@@ -198,20 +194,20 @@ $x$ est l'abscisse du point de contact de la roue avant avec la courbe.
Le vecteur unitaire normal en ce point est :
\begin{equation*}
\vec{n}_{0x}=\frac{1}{\sqrt{1+f'(x)^2}}
-\begin{pmatrix}
--f'(x)\\
-1
-\end{pmatrix}
+\begin{pmatrix}-f'(x)\\1\end{pmatrix}
\end{equation*}
+
Soit $V$ l'axe de la roue avant, son vecteur position a pour coordonnées :
+
\begin{align*}
-\overrightarrow{OV}&=\vec{x}+r\cdot \vec{n}_{0x}\\
-&=\begin{pmatrix}
-x-r\frac{f'(x)}{\sqrt{1+f'(x)^2}}\\
-f(x)+r\frac{1}{\sqrt{1+f'(x)^2}}
-\end{pmatrix}
+\overrightarrow{OV} &= \vec{x}+r\cdot \vec{n}_{0x}\\
+ &=\begin{pmatrix} x-r\frac{f'(x)}{\sqrt{1+f'(x)^2}}\\
+ f(x)+r\frac{1}{\sqrt{1+f'(x)^2}}
+ \end{pmatrix}
\end{align*}
+
Si $R$ est la distance entre les 2 axes :
+
\begin{align*}
|\overrightarrow{OV}-\overrightarrow{OH}|&=R\\
\left|
@@ -226,7 +222,10 @@ f(x)-f(x_0)+r\left(\frac{1}{\sqrt{1+f'(x)^2}}-\frac{1}{\sqrt{1+f'(x_0)^2}}\right
\end{pmatrix}
\right|&=R
\end{align*}
-Nous obtenons une équation en $x$, où $x$ est l'abscisse du point de tangence de la roue avant avec la courbe. La résolution de cette équation fixera la position de la roue avant.
+
+Nous obtenons une équation en $x$, où $x$ est l'abscisse du point de tangence de la roue
+avant avec la courbe. La résolution de cette équation fixera la position de la roue avant.
+
\begin{equation*}
\left(x-x_0+r\left(\frac{f'(x_0)}{\sqrt{1+f'(x_0)^2}}-\frac{f'(x)}{\sqrt{1+f'(x)^2}}\right)\right)^2+\left(f(x)-f(x_0)+r\left(\frac{1}{%
\sqrt{1+f'(x)^2}}-\frac{1}{\sqrt{1+f'(x_0)^2}}\right)\right)^2=R^2
diff --git a/Master/texmf-dist/doc/generic/pst-vehicle/pst-vehicle-doc.pdf b/Master/texmf-dist/doc/generic/pst-vehicle/pst-vehicle-doc.pdf
index 4ba0224abd5..f19ef0ef9dc 100644
--- a/Master/texmf-dist/doc/generic/pst-vehicle/pst-vehicle-doc.pdf
+++ b/Master/texmf-dist/doc/generic/pst-vehicle/pst-vehicle-doc.pdf
Binary files differ
diff --git a/Master/texmf-dist/doc/generic/pst-vehicle/pst-vehicle-doc.tex b/Master/texmf-dist/doc/generic/pst-vehicle/pst-vehicle-doc.tex
index 97fa8996b0f..ec2e9cf97be 100644
--- a/Master/texmf-dist/doc/generic/pst-vehicle/pst-vehicle-doc.tex
+++ b/Master/texmf-dist/doc/generic/pst-vehicle/pst-vehicle-doc.tex
@@ -10,6 +10,8 @@
%% Juergen Gilg
%% Manuel Luque
%%
+%% Herbert Voß (bugfixes)
+%%
%% This program can redistributed and/or modified under %%
%% the terms of the LaTeX Project Public License %%
%% Distributed from CTAN archives in directory %%
@@ -20,24 +22,21 @@
%% `pst-vehicle' is a PSTricks package
%%
%%
-\documentclass[11pt,english,BCOR10mm,DIV12,bibliography=totoc,parskip=false,fleqn,
- smallheadings, headexclude,footexclude,oneside,dvipsnames,svgnames,x11names,distiller]{pst-doc}
-%\documentclass[11pt,english,BCOR10mm,DIV12,bibliography=totoc,parskip=false,smallheadings
-% headexclude,footexclude,oneside,dvipsnames,svgnames,distiller]{pst-doc}
+%% $Id: pst-vehicle-doc.tex 375 2021-12-29 12:04:46Z herbert $
+\RequirePackage{pdfmanagement-testphase}
+\DeclareDocumentMetadata{}
+%
+\documentclass[11pt,english,BCOR=10mm,DIV=12,bibliography=totoc,parskip=false,headings=small,
+ headinclude=false,footinclude=false,oneside]{pst-doc}
\listfiles
+\usepackage{biblatex}
\usepackage[autostyle]{csquotes}
-\usepackage{biblatex}%\usepackage[style=dtk]{biblatex}
\addbibresource{pst-vehicle-doc.bib}
-\usepackage[utf8]{inputenc}
\let\pstvehicleFV\fileversion
\usepackage[e]{esvect} % für schönere Vektorpfeile
\usepackage{pst-vehicle,pst-eucl,pstricks-add,animate}
\let\belowcaptionskip\abovecaptionskip
-
-\usepackage{etex} % um die Anzahl der Register zu erhöhen (sonst nur 256)
-
-
\newcommand{\qrq}{\ensuremath{\quad \Rightarrow \quad}}
\newcommand{\envert}[1]{\left\lvert#1\right\rvert}
\let\abs=\envert
@@ -48,15 +47,13 @@
\makeatletter
\def\curveVal{\def\pst@par{}\pst@object{curveVal}}%
-\def\curveVal@i#1#2{\@ifnextchar[%
-{\curveVal@ii{#1}{#2}}%
-{\curveVal@ii{#1}{#2}[1]}}%
+\def\curveVal@i#1#2{\@ifnextchar[{\curveVal@ii{#1}{#2}}{\curveVal@ii{#1}{#2}[1]}}%
\def\curveVal@ii#1#2[#3]{%
-\pst@killglue%
-\begingroup%
-\use@par%
-\begin@SpecialObj%
-\pst@Verb{%
+ \pst@killglue%
+ \begingroup%
+ \use@par%
+%\begin@SpecialObj%
+ \pst@Verb{%
/Pi 3.1415926 def
/rpn {tx@AlgToPs begin AlgToPs end cvx} def
/x0 #1 def
@@ -85,14 +82,14 @@
/gamma 90 beta add def
/nex gamma cos def
/ney gamma sin def
-}%
-\pnode(!x0 funcx0){PC}%
-\pnode(!x0 deltaxW 2 mul add funcx0 deltayW 2 mul add){QC}%
-\pnode(!x0 deltax0 add funcx0 deltay0 add){MC}%
-\pnode(!x0 deltaxW add funcx0 deltayW add){MW}%
-\showpointsfalse%
-\end@SpecialObj%
-\endgroup\ignorespaces%
+ }%
+ \pnode(!x0 funcx0){PC}%
+ \pnode(!x0 deltaxW 2 mul add funcx0 deltayW 2 mul add){QC}%
+ \pnode(!x0 deltax0 add funcx0 deltay0 add){MC}%
+ \pnode(!x0 deltaxW add funcx0 deltayW add){MW}%
+ \showpointsfalse
+% \end@SpecialObj%
+ \endgroup\ignorespaces
}%
\makeatother
%3 \cdot f' \cdot (f'')^2 - (f')^2 \cdot f''' - f''' = 0 Stellen maximaler Krümmung!
@@ -102,13 +99,12 @@
\def\bgImage{%
\begin{pspicture}(0,0)(14,8)
-\def\FuncA{0.5*cos(1.5*x)+0.25*x}
-\psplot[plotpoints=500]{0}{16}{\FuncA}
-\psVehicle[vehicle=\HighWheeler,showSlope=false,linecolor=Gold]{0.35}{1.2}{\FuncA}%
-\psVehicle[vehicle=\Bike,style=bike,showSlope=false,linecolor=green!70]{0.5}{6}{\FuncA}%
-\psVehicle[vehicle=\Truck,style=truck,showSlope=false]{0.35}{12.2}{\FuncA}%
-\end{pspicture}
-}
+ \def\FuncA{0.5*cos(1.5*x)+0.25*x}
+ \psplot[plotpoints=500]{0}{16}{\FuncA}
+ \psVehicle[vehicle=\HighWheeler,showSlope=false,linecolor=Gold]{0.35}{1.2}{\FuncA}%
+ \psVehicle[vehicle=\Bike,style=bike,showSlope=false,linecolor=green!70]{0.5}{6}{\FuncA}%
+ \psVehicle[vehicle=\Truck,style=truck,showSlope=false]{0.35}{12.2}{\FuncA}%
+\end{pspicture}}
\lstset{language=PSTricks,morekeywords={psVehicle}\footnotesize\ttfamily}
%
@@ -116,26 +112,23 @@
\psset{algebraic=true}
\newpsstyle{quadrillage}{subgriddiv=2,gridlabels=5pt,gridwidth=0.3pt,gridcolor=black!50,subgridwidth=0.2pt,subgridcolor=black}
-\newcommand{\Epkt}[3]{\ensuremath{{\text{#1}}\left(\,#2\;\vline\;#3\,\right)}}
+\newcommand\Epkt[3]{\ensuremath{{\text{#1}}\left(\,#2\;\vline\;#3\,\right)}}
\begin{document}
-\title{pst-vehicle v 1.2}
+\title{pst-vehicle v 1.3}
\subtitle{A PSTricks package for slipping/rolling vehicles on curves of any kind of mathematical functions}
-\author{Thomas \textsc{Söll}\\
-avec la collaboration de\\
-Manuel \textsc{Luque} et Jürgen \textsc{Gilg}}
+\author{Thomas Söll\\Manuel Luque\\Jürgen Gilg\\Herbert Voß (bugfixes)}
\date{\today}
-\maketitle
+\settitle
\tableofcontents
\psset{unit=1cm}
-
-\clearpage
+\newpage
\begin{abstract}
@@ -156,13 +149,13 @@ the License, or (at your option) any later version. %%
\end{abstract}
-\clearpage
-
+\newpage
\section{Theory---the mathematical background}
-Within the following first sections, we like to show the theory on how we programmed the package. Easy elementary vector geometry with some basic calculus aspects.
+Within the following first sections, we like to show the theory on how we programmed
+the package. Easy elementary vector geometry with some basic calculus aspects.
@@ -205,15 +198,15 @@ x_0\\
f(x_0)
\end{pmatrix}
\end{equation*}
+
The direction of the tangent line is:
+
\begin{equation*}
-\vec{t}_0=
-\begin{pmatrix}
-1\\
-f'(x_0)
-\end{pmatrix}
+\vec{t}_0= \begin{pmatrix} 1\\ f'(x_0) \end{pmatrix}
\end{equation*}
+
The normed normal vector in $x_0$ is:
+
\begin{equation*}
\vec{n}_{0x_0}=\frac{1}{\sqrt{1+f'(x_0)^2}}
\begin{pmatrix}
@@ -270,6 +263,8 @@ This leads to an equation of the variable $x$, where $x$ is the abscissa of the
+
+
\subsection{Wheels on a curve---different radii}
\psset{saveNodeCoors,NodeCoorPrefix=n,algebraic}
@@ -400,6 +395,7 @@ This leads to an equation of the variable $x$, where $x$ is the abscissa of the
\pcline[linecolor=gray,linestyle=dashed](H)(!nHx nVy)\nbput{$r_1-r_2$}
\pcline[linecolor=gray,linestyle=dashed](!nHx nVy)(!nVx nVy)\nbput{$\sqrt{R^2-(r_1-r_2)^2}$}
+%$
\pnode(!nHx nVy){X}
\pstMarkAngle[linecolor=red,arrows=->,MarkAngleRadius=4.5,LabelSep=3.6]{H}{V}{X}{\color{red}$\alpha$}
@@ -442,6 +438,7 @@ If the plane is not horizontal, there is an additional angle $\beta$ given by th
\pcline[linecolor=gray,linestyle=dashed](H)(!nHx nVy)\nbput{$r_1-r_2$}
\pcline[linecolor=gray,linestyle=dashed](!nHx nVy)(!nVx nVy)\nbput{$\sqrt{R^2-(r_1-r_2)^2}$}
+%$
\pnode(!nHx nVy){X}
\pstMarkAngle[linecolor=red,arrows=->,MarkAngleRadius=4.5,LabelSep=3.6]{H}{V}{X}{\color{red}$\alpha$}
@@ -487,6 +484,9 @@ The total angle $\gamma$ is:
+
+
+
\subsection{Determination of the curvature radius}
A curved curve can be imagined from many small circular arcs. The radius of the respective associated circles is referred to as the radius of curvature. The stronger the curvature of a curve changes, the smaller the intervals have to be chosen in
@@ -554,69 +554,75 @@ Using $\Delta x_{m} = -\frac{f'(x_{0})}{f''(x_{0})}\cdot \left\{ 1 + \left[f'(x_
\subsection{Rolling without slipping}
\begin{pspicture}[showgrid=false,shift=0,saveNodeCoors,NodeCoorPrefix=n](0,-0.8)(18,11)
-\def\funkg{0.4*(x-3)*sin(0.2*(x-5))}
-\curveVal{7}{\funkg}[3]
-%\psplot[algebraic=true,plotpoints=500,linecolor=black,linewidth=2pt,yMaxValue=25,yMinValue=-15]{0}{18}{\funkg}
-\pcline[linewidth=1.5pt,nodesepB=0,linecolor=BrickRed](PC)(MC)
-\psdot[dotsize=5pt](MC)
-\uput{0.2}[40]{0}(MC){M$_{\text{c}}$}
-\psarc[linewidth=1.5pt,linecolor=cyan](MC){!Rhox0}{255}{340}
-\psdot[dotsize=5pt](PC)
-\uput{0.25}[-60]{0}(PC){P}
-\uput{0.25}[60]{0}(QC){Q}
-\uput{0.3}[-100]{0}(MW){M$_{\text{w}}$}
-\pnode([offset=1.3cm]{MC}PC){PCO}
-\pnode([offset=-1.3cm]{PC}MC){MCO}
-\pnode([offset=-1.3cm]{PC}MW){MWO}
-\psline[linewidth=1.5pt](MWO)(MW)
-\psline[linewidth=1.5pt](MCO)(MC)
-\pcline[offset=-5pt,linewidth=1.5pt,linecolor=BrickRed]{<->}(MWO)(MCO)
-\ncput*{\color{BrickRed}$R=\rho - r$}
-\psdot[dotsize=5pt](QC)
-\psdot[dotsize=5pt](MW)
-\pscircle[linewidth=1.5pt](MW){!rW}
-\psarcn[linewidth=1.5pt,linecolor=BrickRed]{->}(MW){!rW 0.5 add}{180}{150}
-\uput{3.65}[165]{0}(MW){$\omega=\dot{\varphi}$}
-%\multido{\iC=0+1}{11}{%
-%\definecolor[ps]{rainbow}{hsb}{0.9 \iC\space 15 div sub 0.95 0.7 }%
-%\rput{!-90 \iC\space 0.5 mul 180 mul Pi div rW div sub alpha sub}(MW){\psline[linewidth=1.5pt,linecolor=rainbow](!rW 0)(!rW 0.2 sub 0)}
-%\rput{!-90 \iC\space 0.5 mul 180 mul Pi div Rhox0 div sub alpha sub}(MC){\psline[linewidth=1.5pt,linecolor=rainbow](!Rhox0 0)(!Rhox0 0.2 add 0)}
-%}
-%%\rput(MW){\psline[linewidth=1.5pt]{->}(0,0)(!tex 4 mul tey 4 mul)}
-\rput{!beta}(MW){\pcline[linewidth=1.2pt,linecolor=BrickRed]{->}(0,0)(2,0)\nbput[npos=0.7]{\color{BrickRed}$\vv{v_{\text{c}}}$}}
-\rput{0}(MC){\uput{!Rho}[-19]{0}(0,0){\color{cyan}G$_{f}$}}
-\rput{-40}(MC){\pnode(!Rho rW sub 0){MWI}}
-\rput{-40}(MC){\pnode(!Rho 0){PCI}}
-\pscircle[linewidth=1.2pt,linecolor=gray,linestyle=dashed](MWI){!rW}
-\psarc[linewidth=1.5pt,linecolor=gray,linestyle=dashed](MC){!Rhox0 rW sub}{290}{330}
-\pcline[linewidth=1pt,nodesepB=0,linecolor=cyan!60,linestyle=dashed](PCI)(MC)
-\pcline[linewidth=1.5pt,nodesepB=0,linecolor=gray,linestyle=dashed](MWI)(MC)
-\psdot[dotsize=5pt,linecolor=gray](MWI)
-\psdot[dotsize=5pt,linecolor=gray](PCI)
-\uput{0.3}[-20]{0}(PCI){$\text{P}'$}
-\uput{0.3}[0]{0}(MWI){$\text{M}_{\text{w}}'$}
-\multido{\iC=0+1}{11}{%
-\definecolor[ps]{rainbow}{hsb}{0.9 \iC\space 15 div sub 1 \iC\space 11 div sub 0.7 }%
-\rput{!-90 \iC\space 0.5 mul 180 mul Pi div rW div sub -50 sub}(MWI){\psline[linewidth=1.5pt,linecolor=rainbow](!rW 0)(!rW 0.2 sub 0)}
-\rput{!-90 \iC\space 0.5 mul 180 mul Pi div Rhox0 div sub -50 sub}(MC){\psline[linewidth=1.5pt,linecolor=rainbow](!Rhox0 0)(!Rhox0 0.2 add 0)}
-}
-%\multido{\iC=0+1}{11}{%
-%\rput{!-90 \iC\space 0.5 mul 180 mul Pi div rW div sub alpha sub 50 gamma sub Rhox0 mul rW div sub}(MWI){\psline[linewidth=1.5pt,linecolor=gray!50](!rW 0)(!rW 0.2 sub 0)}
-%}
-\rput{!beta}(PC){\pcline[linewidth=2pt,linecolor=Green]{->}(0,0)(1.5,0)\nbput[npos=0.7,nrot={!beta neg}]{\color{Green}$\vv{e_{\text{t}}}$}}
-\rput{!gamma}(PC){\pcline[linewidth=2pt,linecolor=Green]{->}(0,0)(1.5,0)\nbput[npos=0.7,nrot={!gamma neg}]{\color{Green}$\vv{e_{\text{n}}}$}}
+ \def\funkg{0.4*(x-3)*sin(0.2*(x-5))}
+ \curveVal{7}{\funkg}[3]
+ %\psplot[algebraic=true,plotpoints=500,linecolor=black,linewidth=2pt,yMaxValue=25,yMinValue=-15]{0}{18}{\funkg}
+ \pcline[linewidth=1.5pt,nodesepB=0,linecolor=BrickRed](PC)(MC)
+ \psdot[dotsize=5pt](MC)
+ \uput{0.2}[40]{0}(MC){M$_{\text{c}}$}
+ \psarc[linewidth=1.5pt,linecolor=cyan](MC){!Rhox0}{255}{340}
+ \psdot[dotsize=5pt](PC)
+ \uput{0.25}[-60]{0}(PC){P}
+ \uput{0.25}[60]{0}(QC){Q}
+ \uput{0.3}[-100]{0}(MW){M$_{\text{w}}$}
+ \pnode([offset=1.3cm]{MC}PC){PCO}
+ \pnode([offset=-1.3cm]{PC}MC){MCO}
+ \pnode([offset=-1.3cm]{PC}MW){MWO}
+ \psline[linewidth=1.5pt](MWO)(MW)
+ \psline[linewidth=1.5pt](MCO)(MC)
+ \pcline[offset=-5pt,linewidth=1.5pt,linecolor=BrickRed]{<->}(MWO)(MCO)
+ \ncput*{\color{BrickRed}$R=\rho - r$}
+ \psdot[dotsize=5pt](QC)
+ \psdot[dotsize=5pt](MW)
+ \pscircle[linewidth=1.5pt](MW){!rW}
+ \psarcn[linewidth=1.5pt,linecolor=BrickRed]{->}(MW){!rW 0.5 add}{180}{150}
+ \uput{3.65}[165]{0}(MW){$\omega=\dot{\varphi}$}
+ %\multido{\iC=0+1}{11}{%
+ %\definecolor[ps]{rainbow}{hsb}{0.9 \iC\space 15 div sub 0.95 0.7 }%
+ %\rput{!-90 \iC\space 0.5 mul 180 mul Pi div rW div sub alpha sub}(MW){\psline[linewidth=1.5pt,linecolor=rainbow](!rW 0)(!rW 0.2 sub 0)}
+ %\rput{!-90 \iC\space 0.5 mul 180 mul Pi div Rhox0 div sub alpha sub}(MC){\psline[linewidth=1.5pt,linecolor=rainbow](!Rhox0 0)(!Rhox0 0.2 add 0)}
+ %}
+ %%\rput(MW){\psline[linewidth=1.5pt]{->}(0,0)(!tex 4 mul tey 4 mul)}
+ \rput{!beta}(MW){\pcline[linewidth=1.2pt,linecolor=BrickRed]{->}(0,0)(2,0)\nbput[npos=0.7]{\color{BrickRed}$\vv{v_{\text{c}}}$}}
+ \rput{0}(MC){\uput{!Rho}[-19]{0}(0,0){\color{cyan}G$_{f}$}}
+ \rput{-40}(MC){\pnode(!Rho rW sub 0){MWI}}
+ \rput{-40}(MC){\pnode(!Rho 0){PCI}}
+ \pscircle[linewidth=1.2pt,linecolor=gray,linestyle=dashed](MWI){!rW}
+ \psarc[linewidth=1.5pt,linecolor=gray,linestyle=dashed](MC){!Rhox0 rW sub}{290}{330}
+ \pcline[linewidth=1pt,nodesepB=0,linecolor=cyan!60,linestyle=dashed](PCI)(MC)
+ \pcline[linewidth=1.5pt,nodesepB=0,linecolor=gray,linestyle=dashed](MWI)(MC)
+ \psdot[dotsize=5pt,linecolor=gray](MWI)
+ \psdot[dotsize=5pt,linecolor=gray](PCI)
+ \uput{0.3}[-20]{0}(PCI){$\text{P}'$}
+ \uput{0.3}[0]{0}(MWI){$\text{M}_{\text{w}}'$}
+ \multido{\iC=0+1}{11}{%
+% \definecolor{rainbow}{hsb}{\directlua{tex.print(0.9-\iC/15)}, \directlua{tex.print(1-\iC/11)}, 0.7}%
+ \definecolor[ps]{rainbow}{hsb}{0.9 \iC\space 15 div sub 1 \iC\space 11 div sub 0.7 }%
+ \rput{!-90 \iC\space 0.5 mul 180 mul Pi div rW div sub -50 sub}(MWI){\psline[linewidth=1.5pt,linecolor=rainbow](!rW 0)(!rW 0.2 sub 0)}
+ \rput{!-90 \iC\space 0.5 mul 180 mul Pi div Rhox0 div sub -50 sub}(MC){\psline[linewidth=1.5pt,linecolor=rainbow](!Rhox0 0)(!Rhox0 0.2 add 0)}
+ }
+ %\multido{\iC=0+1}{11}{%
+ %\rput{!-90 \iC\space 0.5 mul 180 mul Pi div rW div sub alpha sub 50 gamma sub Rhox0 mul rW div sub}(MWI){\psline[linewidth=1.5pt,linecolor=gray!50](!rW 0)(!rW 0.2 sub 0)}
+ %}
+ \rput{!beta}(PC){\pcline[linewidth=2pt,linecolor=Green]{->}(0,0)(1.5,0)\nbput[npos=0.7,nrot={!beta neg}]{\color{Green}$\vv{e_{\text{t}}}$}}
+ \rput{!gamma}(PC){\pcline[linewidth=2pt,linecolor=Green]{->}(0,0)(1.5,0)\nbput[npos=0.7,nrot={!gamma neg}]{\color{Green}$\vv{e_{\text{n}}}$}}
\end{pspicture}
The condition of a rolling wheel without slipping forces, that the center of the wheel needs to make a rotation around the point P. Therefore, the center moves with the velocity:
+
\begin{equation*}
\vv{v_{\text{c}}} = r\cdot \dot{\varphi}\cdot \vv{e_{\text{t}}} \qquad \text{with normed tangent vector } \vv{e_{\text{t}}}
\end{equation*}
+
Cause the center of the wheel also moves along the circle around M$_{\text{c}}$ with radius $\rho - r$ and therefore the point P moves through the distance $\Delta s$ to the point $\text{P}'$---the velocities in M$_\text{w}$ and in P behave
like their corresponding radii:
+
\begin{equation*}
\vv{v_{\text{c}}} = \frac{\rho - r}{\rho}\cdot \frac{\Delta s}{\Delta t} \cdot \vv{e_{\text{t}}} \qquad \text{with very small intervals, thus }\quad \frac{\Delta s}{\Delta t} = \dot{s}
\end{equation*}
+
Equating the right sides of both equations for the velocity of the center of the wheel finally leads to:
+
\begin{equation*}
r\cdot \dot{\varphi} = \frac{\rho - r}{\rho}\cdot \dot{s} \qrq \frac{\text{d}\varphi}{\text{d}t} = \frac{\rho - r}{\rho \cdot r}\cdot \frac{\text{d}s}{\text{d}t} \qrq \text{d}\varphi = \frac{\rho - r}{\rho \cdot r}\cdot \text{d}s = \frac{\rho - r}{\rho
\cdot r}\cdot \sqrt{1+[f'(x)]^{2}} \cdot \text{d}x
@@ -644,6 +650,8 @@ Here follows a list of the vehicles that come along with the package:
+
+
\subsection{\textbackslash Bike}
\begin{LTXexample}[pos=l,width=4cm]
@@ -744,7 +752,9 @@ In this section we present $12$ predefined wheels that can be used for the front
-\subsection{\textbackslash{}wheelB}
+
+
+\subsection{\nxLcs{wheelB}}
\begin{LTXexample}[pos=l,width=2cm]
\begin{pspicture}(-1,-1)(1,1)
@@ -988,7 +998,7 @@ extra_mem_bot = 12000000 % extra low memory for boxes, glue, breakpoints, etc.
\end{LTXexample}
-\clearpage
+%\clearpage
\section{List of all optional arguments for \texttt{pst-vehicle}}
@@ -996,14 +1006,13 @@ extra_mem_bot = 12000000 % extra low memory for boxes, glue, breakpoints, etc.
\xkvview{family=pst-vehicle,columns={key,type,default}}
-\clearpage
-
+%\clearpage
-\nocite{*}
-\bgroup
-\RaggedRight
-\printbibliography
-\egroup
+%\nocite{*}
+%\bgroup
+%\RaggedRight
+%\printbibliography
+%\egroup
\printindex