%% Created by Maple 6 (IBM INTEL NT)
%% Source Worksheet: charplot.mws
%% Generated: Thu Mar 25 11:45:43 2004
\documentclass{article}
\usepackage{maple2e}
 \def\emptyline{\vspace{12pt}}
\DefineParaStyle{Heading 1}
\DefineParaStyle{Heading 3}
\DefineParaStyle{Maple Output}
\DefineParaStyle{Warning}
\DefineCharStyle{2D Math}
\DefineCharStyle{2D Output}
\begin{document}
\pagestyle{empty}
\begin{maplegroup}
\begin{Heading 1}
Reissner-Nordstrom solution
\end{Heading 1}

\begin{Heading 3}
Charged particle
\end{Heading 3}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{restart:}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{f := -Q_^2*u^4
        +2*M*u^3 -(1 +Q_^2*(1-q^2)/L^2)*u^2 +       
2/L^2*(M-q*Q_*E)*u -(1-E^2)/L^2 = 0:}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{u_c := 0.2225: Q_ := .8: M := 1.2: r_c := 1/u_c; q := 2:}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{r_c := 4.494382022;}{%
\[
\mathit{r\_c} := 4.494382022
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{E_c := 1/2*(u_c*q*Q_*(4*M*u_c-1-3*Q_^2*u_c^2)
-sqrt((2*M*u_c-1-Q_^2*u_c^2)^2
*(4-12*M*u_c+8*Q_^2*u_c^2+u_c^2*Q_^2*q^2)))
/(-2*Q_^2*u_c^2+3*M*u_c-1);}{%
}
\end{mapleinput}

\begin{mapleinput}
\mapleinline{active}{1d}{L_c := (u_c*Q_^2-u_c*Q_^2*q^2-M+q*Q_*E_c)
/(u_c*(-2*Q_^2*u_c^2+3*M*u_c-1));}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{E_c := 1.046972868;}{%
\[
\mathit{E\_c} := 1.046972868
\]
%
}
\end{maplelatex}

\begin{maplelatex}
\mapleinline{inert}{2d}{L_c := -.8214996932;}{%
\[
\mathit{L\_c} := -.8214996932
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{L := 6: E := 1.1:}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{u := solve(f);}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{u := -.8570880353e-1, .6863713358e-1, .4699066176, 3.297165052;}{%
\[
u := -.08570880353, \,.06863713358, \,.4699066176, \,3.297165052
\]
%
}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{ph1 := g *(EllipticF(arcsin(sqrt((u[4]-u[2]) *(y-u[1]) /(u[2]-u[1])
/(u[4]-y))), k) +EllipticK(k))/Q_:}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{ph2 := g *EllipticF(arcsin(sqrt((u[4]-u[2]) *(y-u[3]) /(u[4]-u[3])
/(y-u[2]))), k)/Q_:}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{g := 2/sqrt((u[4]-u[2])*(u[3]-u[1])):}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{k := sqrt((u[4]-u[3])*(u[2]-u[1])/(u[4]-u[2])/(u[3]-u[1])); }{%
}should be \TEXTsymbol{<} or = 1.
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\mapleinline{inert}{2d}{k := .4932202926;}{%
\[
k := .4932202926
\]
%
}
\end{maplelatex}

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

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

\mapleresult
\begin{maplettyout}
Warning, the name changecoords has been redefined
\end{maplettyout}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{Fi1 := polarplot([r, ph1, y = u[1]..u[2]], -12..12, -30..30,
thickness = 3, color = blue):}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{Fi2 := polarplot([r, -ph1, y = u[1]..u[2]], thickness = 3, color =
blue):}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{Se := polarplot([r, ph2, y = u[3]..u[4]], thickness = 3, color =
blue):}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{rC := polarplot(r_c, color = blue):}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{plotsetup(ps, plotoutput = `charplot.eps`, plotoptions = `color,
portrait, noborder`):}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{display(\{Fi1, Fi2, Se, rC\}, axes = frame, scaling =
constrained);}{%
}
\end{mapleinput}

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

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