%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\stt{\tt}

%\def\sttT{\small {\tt T}}
\def\sttT{{\tt T}}

\def\sttp{p}
\def\sttq{q}
\def\sttt{t}
\def\sttqd{\dot{q}}

\def\subzero{{0}}
\def\subone{{1}}
\def\subtwo{{2}}
\def\subthree{{3}}

\def\lu{\left(}
\def\ru{\right)}
\def\ld{\left[}
\def\rd{\right]}

%\def\lu{{\left \lceil}}
%\def\ru{{\right \rceil}}
%\def\ld{{\left \lfloor}}
%\def\rd{{\right \rfloor}}

%\def\partialq{\partial_q}
%\def\partialqd{\partial_{\dot q}}
%\def\partialp{\partial_p}
%\def\partialt{\partial_t}
%\def\partialT{\partial_T}

%\def\partialq{\partial_{x}}
%\def\partialqd{\partial_{v}}
%\def\partialp{\partial_{m}}
%\def\partialt{\partial_{t}}
%\def\partialT{\partial_T}

%\def\partialq{\partial_{\small Q}}
%\def\partialqd{\partial_{\small \dot{Q}}}
%\def\partialp{\partial_{\small P}}
%\def\partialt{\partial_{\small T}}
%\def\partialT{\partial_{T_t}}

%\def\partialq{\partial_{\small {\sf q}}}
%\def\partialqd{\partial_{\dot{\small {\sf q}}}}
%\def\partialp{\partial_{\small {\sf p}}}
%\def\partialt{\partial_{\small {\sf t}}}
%\def\partialT{\partial_{\small {\sf T}}}

%\def\partialq{\partial_{\sf q}}
%\def\partialqd{\partial_{\dot{\sf q}}}
%\def\partialqdd{\partial_{\ddot{\sf q}}}
%\def\partialp{\partial_{\sf p}}
%\def\partialt{\partial_{\sf t}}
%\def\partialT{\partial_{\sf T}}
%\def\partialz{\partial_{\sf z}}

\def\partialq{\partial_\subone}
\def\partialqd{\partial_\subtwo}
\def\partialqdd{\partial_\subthree}
\def\partialp{\partial_\subtwo}
\def\partialt{\partial_\subzero}
\def\partialT{\partial_{\sf T}}
\def\partialz{\partial_\subone}

\def\Pt{(partial 0)}
\def\Pq{(partial 1)}
\def\Pqdot{(partial 2)}
\def\Pp{(partial 2)}

\newcommand{\LE}{{\sf E}}

%\def\partialq{\partial_q}
%\def\partialqd{\partial_{\dot q}}
%\def\partialp{\partial_p}
%\def\partialt{\partial_t}
%\def\partialT{\partial_T}

\def\partialfirst{\partial_0}
\def\partialsecond{\partial_1}
\def\partialthird{\partial_2}

\def\partialN{\partial_N}

% phase space derivative
\def\Dps{D_s}

% for particle indexing in sums
\def\indexa{\alpha}  
\def\indexb{\beta}

\def\half{\textstyle \frac{1}{2}}
%\def\half{\frac{1}{2}}

\def\caret{\^\,\hspace{-2pt}}

%\def\fdef{:=}
\def\fdef{\triangleq}

\newcommand{\qed}{$\ $\rule{2.5mm}{2.5mm}}

\newcommand{\be}{\begin{equation}}  %numbered equations
\newcommand{\ee}{\end{equation}}
\newcommand{\bea}{\begin{eqnarray}}  %numbered equations
\newcommand{\eea}{\end{eqnarray}}
\newcommand{\beas}{\begin{eqnarray*}}
\newcommand{\eeas}{\end{eqnarray*}}
\newcommand{\bl}{\begin{lisp}}
\newcommand{\el}{\end{lisp}}
\newcommand{\bls}{\begin{lisp*}}
\newcommand{\els}{\end{lisp*}}

\newcommand{\bfomega}{\mbox{\boldmath $\omega$}}
\newcommand{\bfalpha}{\mbox{\boldmath $\alpha$}}
\newcommand{\bflambda}{\mbox{\boldmath $\lambda$}}
\newcommand{\bfxi}{\mbox{\boldmath $\xi$}}
\newcommand{\bv}{\begin{verbatim}{}}
\newcommand{\ev}{\end{verbatim}{}}

% for orientation vector stuff
\def\orientationr{o}
\def\orientationx{o_x}
\def\orientationy{o_y}
\def\orientationz{o_z}

\newcommand{\dddot}[1]{
\begin{picture}(7,9)
\put(1,9){\circle*{1}}
\put(3,9){\circle*{1}}
\put(5,9){\circle*{1}}
\put(0,0){$#1$}
\end{picture}}

\newcommand{\Chart}{
\begin{picture}(8.5,7.5)
\put(1,0){\line(0,0){8}}
\put(4,0){\line(0,0){8}}
\put(7,0){\line(0,0){8}}
\put(0,1){\line(1,0){8}}
\put(0,4){\line(1,0){8}}
\put(0,7){\line(1,0){8}}
\end{picture}}

% \newcommand{\Chart}{
% \begin{picture}(8.5,7.5)
% \put(0,0){\line(0,0){8}}
% \put(3,0){\line(0,0){8}}
% \put(6,0){\line(0,0){8}}
% \put(-1,1){\line(1,0){8}}
% \put(-1,4){\line(1,0){8}}
% \put(-1,7){\line(1,0){8}}
% \end{picture}}

\newcommand{\PPChart}{
\begin{picture}(8.5,7.5)
\put(2,0){\line(0,0){8}}
\put(4,0){\line(0,0){8}}
\put(-1,1){\line(1,0){8}}
\put(-1,4){\line(1,0){8}}
\put(-1,7){\line(1,0){8}}
\end{picture}}

\newcommand{\PChart}{
\begin{picture}(8.5,7.5)
\put(1,0){\line(0,0){8}}
\put(5,0){\line(0,0){8}}
\put(-1,1){\line(1,0){8}}
\put(-1,4){\line(1,0){8}}
\put(-1,7){\line(1,0){8}}
\end{picture}}

\def\boxit#1{\vbox{\hrule\hbox{\vrule\kern5pt
     \vbox{\kern5pt#1\kern5pt}\kern3pt\vrule}\hrule}}
\newcommand{\wideprime}[1]{#1^\prime}
\newcommand{\nprime}[1]{#1^\prime}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\za{$\pi/2$}
\def\zb{$\pi$}
\def\zc{$2\pi$}
\def\zd{$-\pi$}

\def\putmbox#1#2#3{\put(#1){\makebox(0,0)[#2]{#3}}}
\def\putpsfile#1{\put(0,0){\special{psfile={#1}}}}

\newcommand{\e}[1]{\times 10^{#1}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\noepigraph{\begin{epigraph}\addvspace{6pc}\end{epigraph}}
