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-rw-r--r--Master/texmf-dist/doc/generic/pst-vehicle/pst-vehicle-doc.tex53
1 files changed, 34 insertions, 19 deletions
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 6a04bb3dfad..97fa8996b0f 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
@@ -5,7 +5,7 @@
%%
%% Package `pst-vehicle.tex'
%%
-%% Thomas S\"{o}ll
+%% Thomas Söll
%% with the collaboration of
%% Juergen Gilg
%% Manuel Luque
@@ -29,13 +29,13 @@
\usepackage{biblatex}%\usepackage[style=dtk]{biblatex}
\addbibresource{pst-vehicle-doc.bib}
\usepackage[utf8]{inputenc}
-\let\pstpersFV\fileversion
-\usepackage[e]{esvect} % f\"{u}r sch\"{o}nere Vektorpfeile
+\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 erh\"{o}hen (sonst nur 256)
+\usepackage{etex} % um die Anzahl der Register zu erhöhen (sonst nur 256)
\newcommand{\qrq}{\ensuremath{\quad \Rightarrow \quad}}
@@ -95,7 +95,7 @@
\endgroup\ignorespaces%
}%
\makeatother
-%3 \cdot f' \cdot (f'')^2 - (f')^2 \cdot f''' - f''' = 0 Stellen maximaler Kr\"{u}mmung!
+%3 \cdot f' \cdot (f'')^2 - (f')^2 \cdot f''' - f''' = 0 Stellen maximaler Krümmung!
\psset{arrowlength=2.8,arrowinset=0.1}
@@ -122,11 +122,11 @@
\begin{document}
-\title{pst-vehicle v 1.1}
+\title{pst-vehicle v 1.2}
\subtitle{A PSTricks package for slipping/rolling vehicles on curves of any kind of mathematical functions}
-\author{Thomas \textsc{S\"{o}ll}\\
+\author{Thomas \textsc{Söll}\\
avec la collaboration de\\
-Manuel \textsc{Luque} et J\"{u}rgen \textsc{Gilg}}
+Manuel \textsc{Luque} et Jürgen \textsc{Gilg}}
\date{\today}
\maketitle
@@ -139,8 +139,11 @@ Manuel \textsc{Luque} et J\"{u}rgen \textsc{Gilg}}
\begin{abstract}
-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\,\%. 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.
-The line connecting the two contact points from the front and the rear wheel with the curve and the sign of the slope can be easily displayed. It is also possible to represent, not a speed-o-meter of the vehicle, but a slope-o-meter was introduced as an indicator of the value of the slope of the straight line defined above.
+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\,\%. 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.
+The line connecting the two contact points from the front and the rear wheel with the curve and the sign of the slope can be easily displayed. It is also possible to represent, not a speed-o-meter of the vehicle, but a slope-o-meter was
+introduced as an indicator of the value of the slope of the straight line defined above.
\vfill
@@ -486,9 +489,11 @@ 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 order to be able to speak approximately of a circular arc.
+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
+order to be able to speak approximately of a circular arc.
-To find the radius of such an arc and thus the radius of the curvature of the curve at a point $x_{0}$, the normal in $ x_{0} $ should be intersected with the normal in $x_{0}+\epsilon$. This yields the $x$ value of the center of the curvature circle M of the curve. The following drawing is intended to illustrate this.
+To find the radius of such an arc and thus the radius of the curvature of the curve at a point $x_{0}$, the normal in $ x_{0} $ should be intersected with the normal in $x_{0}+\epsilon$. This yields the $x$ value of the center of the curvature circle
+M of the curve. The following drawing is intended to illustrate this.
\begin{pspicture}[showgrid=false,shift=0,saveNodeCoors,NodeCoorPrefix=n](0,-0.6)(18,9.2)
\def\funkg{0.4*(x-3)*sin(0.2*(x-5))}
@@ -520,8 +525,10 @@ To find the radius of such an arc and thus the radius of the curvature of the cu
\makebox[7cm][l]{\textbf{Intersection point of the normals:}} $n_{\epsilon}(x) - n(x) = 0$
\begin{alignat*}{2}
- \frac{x}{f'(x_{0}+\epsilon)} + \frac{x_{0}}{f'(x_{0}+\epsilon)} + \frac{\epsilon}{f'(x_{0}+\epsilon)} + f(x_{0}+\epsilon) + \frac{x}{f'(x_{0})} - \frac{x_{0}}{f'(x_{0})} - f(x_{0}) & = 0&\qquad& \\[4pt]
-\frac{x\cdot \left[f'(x_{0}+\epsilon) - f'(x_{0})\right]}{f'(x_{0}+\epsilon)\cdot f'(x_{0})} - \frac{x_{0}\cdot \left[f'(x_{0}+\epsilon) - f'(x_{0})\right]}{f'(x_{0}+\epsilon)\cdot f'(x_{0})} + \frac{\epsilon}{f'(x_{0}+\epsilon)} + f(x_{0}+\epsilon) - f(x_{0}) & = 0&\qquad& |:\epsilon\\[4pt]
-\frac{x\cdot \frac{f'(x_{0}+\epsilon) - f'(x_{0})}{\epsilon}}{f'(x_{0}+\epsilon)\cdot f'(x_{0})} - \frac{x_{0}\cdot \frac{f'(x_{0}+\epsilon) - f'(x_{0})}{\epsilon}}{f'(x_{0}+\epsilon)\cdot f'(x_{0})} + \frac{1}{f'(x_{0}+\epsilon)} + \frac{f(x_{0}+\epsilon) - f(x_{0})}{\epsilon} & = 0&\qquad&| \lim_{\epsilon\to 0}\\[4pt]
+\frac{x\cdot \left[f'(x_{0}+\epsilon) - f'(x_{0})\right]}{f'(x_{0}+\epsilon)\cdot f'(x_{0})} - \frac{x_{0}\cdot \left[f'(x_{0}+\epsilon) - f'(x_{0})\right]}{f'(x_{0}+\epsilon)\cdot f'(x_{0})} + \frac{\epsilon}{f'(x_{0}+\epsilon)} + f(x_{0}+\epsilon) - f(x_{0}) & =
+0&\qquad& |:\epsilon\\[4pt]
+\frac{x\cdot \frac{f'(x_{0}+\epsilon) - f'(x_{0})}{\epsilon}}{f'(x_{0}+\epsilon)\cdot f'(x_{0})} - \frac{x_{0}\cdot \frac{f'(x_{0}+\epsilon) - f'(x_{0})}{\epsilon}}{f'(x_{0}+\epsilon)\cdot f'(x_{0})} + \frac{1}{f'(x_{0}+\epsilon)} + \frac{f(x_{0}+\epsilon) -
+f(x_{0})}{\epsilon} & = 0&\qquad&| \lim_{\epsilon\to 0}\\[4pt]
\frac{x\cdot f''(x_{0})}{f'(x_{0})\cdot f'(x_{0})} - \frac{x_{0}\cdot f''(x_{0})}{f'(x_{0})\cdot f'(x_{0})} + \frac{1}{f'(x_{0})} + f'(x_{0}) & = 0&&
\end{alignat*}
Solving for $x$:
@@ -604,13 +611,15 @@ The condition of a rolling wheel without slipping forces, that the center of the
\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:
+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
+ 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
\end{equation*}
@@ -619,7 +628,9 @@ Equating the right sides of both equations for the velocity of the center of the
This package contains a number of predefined vehicles, like \emph{Bike}, \emph{Tractor}, \emph{Highwheeler}, \emph{Truck}, \emph{Segway}, \emph{Unicycle}. The last two of the vehicles only contain one axis, the rest has two axes.
-Except the mono-cycles, a vehicle is defined by the radius of each wheel, [\texttt{rB}] for the rear (back) wheel and [\texttt{rF}] for the front wheel and the distance [\texttt{d}] between the axes of the two wheels. Their values must be given within the options of the \texttt{\textbackslash psVehicle [options]} command. The cladding of a vehicle, auto body or bicycle frame must of course be adapted to the dimensions indicated above. A number of types of wheels and vehicles have been predefined.
+Except the mono-cycles, a vehicle is defined by the radius of each wheel, [\texttt{rB}] for the rear (back) wheel and [\texttt{rF}] for the front wheel and the distance [\texttt{d}] between the axes of the two wheels. Their values must be given
+within the options of the \texttt{\textbackslash psVehicle [options]} command. The cladding of a vehicle, auto body or bicycle frame must of course be adapted to the dimensions indicated above. A number of types of wheels and vehicles have
+been predefined.
We also setup some \verb+\newpsstyle+ for each of the vehicles, where the dimensions and the choice of the wheels are setup like we would choose them.
\begin{lstlisting}
@@ -853,7 +864,8 @@ This package offers the following command:
\textbf{Important note:} The function has to be given in algebraic notation and not in RPN.
-The package \LPack{pst-vehicle} contains the options \nxLkeyword{epsilon=}, \nxLkeyword{rB=}, \nxLkeyword{rF=}, \nxLkeyword{d=}, \nxLkeyword{gang=}, \nxLkeyword{vehicle=}, \nxLkeyword{ownvehicle=}, \nxLkeyword{backwheel=}, \nxLkeyword{frontwheel=}, \nxLkeyword{MonoAxis=}, \nxLkeyword{showSlope=} and \nxLkeyword{startPos=}
+The package \LPack{pst-vehicle} contains the options \nxLkeyword{epsilon=}, \nxLkeyword{rB=}, \nxLkeyword{rF=}, \nxLkeyword{d=}, \nxLkeyword{gang=}, \nxLkeyword{vehicle=}, \nxLkeyword{ownvehicle=}, \nxLkeyword{backwheel=},
+\nxLkeyword{frontwheel=}, \nxLkeyword{MonoAxis=}, \nxLkeyword{showSlope=} and \nxLkeyword{startPos=}
\begin{quote}
\begin{tabularx}{\linewidth}{ @{} l >{\ttfamily}l X @{} }\toprule
\emph{Name} & \emph{Default} & \emph{Meaning} \\\midrule
@@ -869,6 +881,7 @@ The package \LPack{pst-vehicle} contains the options \nxLkeyword{epsilon=}, \nxL
\Lkeyword{MonoAxis} & false & if the vehicle has one axis\\
\Lkeyword{showSlope} & true & showing the slope of the vehicle\\
\Lkeyword{startPos} & 0 & synchronizing the initial rotation of the wheels at the start point\\
+\Lkeyword{GravNode} & dA12 2 div 1 & sets a node near center of gravity by default with name GravC\\
\bottomrule
\end{tabularx}
\end{quote}
@@ -902,6 +915,8 @@ This command is shipped with two arguments to customize it with the \emph{color
\psgrid[style=quadrillage](1,1)(8,6)
\psplot{1}{8}{\FuncA}
\psVehicle[vehicle=\Truck,showSlope=false,frontwheel=\wheelC,backwheel=\arrowWheel,rB=1,rF=1]{0.5}{3.2}{\FuncA}
+\psdot(GravC)
+\psline[arrowscale=1.5]{->}(GravC)([offset=-2]GravC)
\end{pspicture}
\end{LTXexample}
@@ -992,4 +1007,4 @@ extra_mem_bot = 12000000 % extra low memory for boxes, glue, breakpoints, etc.
\printindex
-\end{document} \ No newline at end of file
+\end{document}