%% Created by Maple 6 (IBM INTEL NT)
%% Source Worksheet: nucircst2.mws
%% Generated: Sun Apr 27 15:13:37 2003
%\documentclass{article}
%\usepackage{maple2e}
 \def\emptyline{\vspace{12pt}}
\DefineParaStyle{Heading 1}
\DefineParaStyle{Heading 2}
\DefineParaStyle{Heading 3}
\DefineParaStyle{Heading 4}
\DefineParaStyle{Maple Output}
\DefineParaStyle{Warning}
\DefineCharStyle{2D Comment}
\DefineCharStyle{2D Math}
\DefineCharStyle{2D Output}
%\begin{document}
%\pagestyle{empty}
\begin{maplegroup}
\begin{Heading 1}
Reissner-Nordstrom solution
\end{Heading 1}
\nopagebreak[3]
\begin{Heading 2}
Null geodesics
\end{Heading 2}
\nopagebreak[3]
\begin{Heading 3}
Double root - unstable circular orbit
\end{Heading 3}
\nopagebreak[3]
\begin{Heading 4}
\mapleinline{inert}{2d}{Q_^2 = 9*M^2/8;}{%
$\mathit{Q\_}^{2}=\frac {9\,M^{2}}{8}$%
}
\end{Heading 4}
\nopagebreak[2]
\begin{mapleinput}
\mapleinline{active}{1d}{restart:}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{ph := 2 *sqrt(b*xi-Q_^2) /b:}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{b := 2 *(M-2*Q_^2*u_c):}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{r := 1/u:}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{u_c := 1/r_cr:}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{r_cr := 1.5*M:}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{Q_ := 0.8: M:= sqrt(8*Q_^2/9):}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{u := 1/xi +u_c:}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{with(plots):}{%
}
\end{mapleinput}

\mapleresult\vspace{-5mm}{\color{blue}
\begin{maplettyout}
Warning, the name changecoords has been redefined
\end{maplettyout}}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{-1/u_c;}{%
}
\end{mapleinput}

\begin{flushleft}
\vspace{-5mm}\hspace{18pt}\mapleinline{inert}{2d}{xi;}{%
$\xi $%
} must not exceed this
\end{flushleft}

\mapleresult\vspace{-5mm}
\begin{maplelatex}
\mapleinline{inert}{2d}{-1.131370850;}{%
\[\color{blue}
-1.131370850
\]
%
}
\end{maplelatex}
\bigskip
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{Fi := polarplot([r, ph, xi = -30..-1.14], -2.5..1.5,
-7..2, color = blue, thickness = 3, numpoints = 300):}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{rC := polarplot(r_cr, linestyle = 2, color = black):}{%
}
\end{mapleinput}
\bigskip
\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{plotsetup(ps, plotoutput = `nullcst2.eps`, plotoptions =
`color, portrait, noborder`):}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{display(\{Fi, rC\}, axes = frame, scaling = constrained);}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\end{mapleinput}

\end{maplegroup}
%\end{document}
%% End of Maple 6 Output
