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\begin{equation*}
  \aligned
  m \ddot x &= F_1 \cos\theta - F_2 \sin\theta - c \dot x, \\
  m \ddot y &= F_1 \sin\theta + F_2 \cos\theta - m g - c \dot y, \\
  J \ddot \theta &= r F_1.
  \endaligned
\end{equation*}
\end{document}