Here is one way, using a stack. The top set are your originals; the bottom set are my replacement, "without changing their format," as requested.
\documentclass{article}
\usepackage{stackengine}
\stackMath
\begin{document}
\begin{center}
$\dot{R}=\frac{66}{364}\ P_R+ \frac{\partial V}{\partial P_R}\qquad
\dot{\theta}=2P_{\theta}(\frac{13}{168r^2}-\frac{33}{364R^2})+\frac{\partial V}{\partial P_{\theta}}$
\end{center}
\begin{center}
$\dot{P_{\theta}}=-\frac{\partial V}{\partial \theta}\qquad
\dot{P_R}=\frac{66P^2_{\theta}}{364R^3}-\frac{\partial V}{\partial R}$
\end{center}
\begin{equation}
\stackanchor[10pt]{
\dot{R}=\frac{66}{364}\ P_R+ \frac{\partial V}{\partial P_R}\qquad
\dot{\theta}=2P_{\theta}(\frac{13}{168r^2}-\frac{33}{364R^2})+\frac{\partial V}{\partial P_{\theta}}
}{
\dot{P_{\theta}}=-\frac{\partial V}{\partial \theta}\qquad
\dot{P_R}=\frac{66P^2_{\theta}}{364R^3}-\frac{\partial V}{\partial R}
}
\end{equation}
\end{document}

For a slightly altered presentation, here is a tabular stack, wherein the columns are individually centered:
\documentclass{article}
\usepackage{tabstackengine}
\stackMath
\begin{document}
\begin{equation}
\setstacktabulargap{2em}
\tabularstackanchor[10pt]{cc}{
\dot{R}=\frac{66}{364}\ P_R+ \frac{\partial V}{\partial P_R}&
\dot{\theta}=2P_{\theta}(\frac{13}{168r^2}-\frac{33}{364R^2})+\frac{\partial V}{\partial P_{\theta}}
}{
\dot{P_{\theta}}=-\frac{\partial V}{\partial \theta}&
\dot{P_R}=\frac{66P^2_{\theta}}{364R^3}-\frac{\partial V}{\partial R}
}
\end{equation}
\end{document}
