equation + aligned
\begin{equation}
\left \{
\begin{aligned}
\dot{v}_{x_{i1}} = -k v_{x_{i1}}& + Fx_{i1,i2} - Fx_{(i-1)1,i1}\\
& + Fx_{i1,(i+1)1}\\
\dot{v}_{y_{i1}} = -k v_{y_{i1}}& + Fy_{i1,i2} - Fy_{(i-1)1,i1}\\
& + Fy_{i1,(i+1)1}.
\end{aligned}
\right.
\end{equation}
http://www.eng.kagawa-u.ac.jp/~haruna/memo/TeX/TeXtips.html