documentclass{article}
usepackage{amsmath}
begin{document}
begin{equation} label{eq:system_dynamics_l}
begin{bmatrix}
m_1+m_2 & dfrac{1}{2}m_2 L  \[4mm]
dfrac{1}{2}m_2 L  & dfrac{1}{2}m_2 L^2
end{bmatrix}
begin{bmatrix}
ddot{x} \[4mm] ddot{theta}
end{bmatrix}
+ begin{bmatrix}
b & 0  \[4mm]
0 & c
end{bmatrix}begin{bmatrix}
dot{x} \[4mm] dot{theta}
end{bmatrix}
+begin{bmatrix}
k & 0 \[4mm] 0 & m_2gdfrac{L}{2}
end{bmatrix}begin{bmatrix}
x \[4mm]  theta
end{bmatrix}
=begin{bmatrix}
0 \[4mm]  0
end{bmatrix}
end{equation}
end{document}