\documentclass[12pt]{article}%
\usepackage[left=.7in,right=.7in,top=.9in,bottom=.9in]{geometry}
\usepackage{enumitem,lipsum}
\newenvironment{autobreakeq}
{\begin{itemize}[label={},leftmargin=1em,itemindent=-1em]\raggedright
\item\relax$}
{$\end{itemize}}
\begin{document}
\lipsum*[2]
\begin{autobreakeq}
a_y =a_Y-2 \xi \theta ' \sin (\theta ) \psi ' \sin (\phi ) \cos (\phi
)-\xi (\theta ')^2 \cos ^2(\phi )-\frac{1}{4} \xi
\cos (2 \theta ) (\psi ')^2-2 \xi \cos (\theta ) \psi
' \phi '+\frac{1}{2} \xi \sin ^2(\theta ) (\psi ')^2