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\begin{document}
\begin{equation*}
  \aligned
    \dot{\alpha}_f &= M_f^{-1}(K_f + \tilde{K}_o)^{-1} 
      \begin{bmatrix} - \omega_y \\ \omega_x \end{bmatrix}
      \\
    \dot{\alpha}_o &= M_o^{-1}R_\psi(K_f + \tilde{K}_o)^{-1}
     \begin{bmatrix} - \omega_y \\ \omega_x \end{bmatrix} \\ 
    \dot{\psi} &= T_f M_f \dot{\alpha}_f + T_o M_o \dot{\alpha}_o.\\
  \endaligned
\end{equation*}
\end{document}