\begin{subequations}
\begin{align}
H^&=\left[
\begin{array}{ccc}
-2 \left(-L_y \left(p q_2-r q_0\right)-L_z \left(q q_0+p q_3\right)+L_x \left(q q_2+r q_3\right)\right) & 2 \left(L_x \left(r q_0+q q_1\right)-L_z
\left(p q_0-q q_3\right)-L_y \left(p q_1+r q_3\right)\right) & -2 \left(L_x \left(q q_0-r q_1\right)+L_z \left(p q_1+q q_2\right)-L_y \left(p q_0+r q_2\right)\right) \\
\left(r L_x-p L_z\right) q_2+\left(p L_y-q L_x\right) q_3 & -2 \left(p L_y-q L_x\right) q_0+2 \left(p L_z-r L_x\right) q_1+\left(q L_z-r L_y\right) q_2
& 2 L_x \left(r q_0+q q_1\right)+L_z \left(q q_3-2 p q_0\right)-L_y \left(2 p q_1+r q_3\right) \\
L_x \left(r q_1-2 q q_0\right)-L_z \left(p q_1+2 q q_2\right)+2 L_y \left(p q_0+r q_2\right) & \left(q L_z-r L_y\right) q_1+\left(p L_y-q L_x\right) q_3
& -2 \left(q L_z-r L_y\right) q_0-2 \left(p L_y-q L_x\right) q_2+\left(r L_x-p L_z\right) q_3 \\
2 \left(p L_z-r L_x\right) q_0+\left(p L_y-q L_x\right) q_1-2 \left(q L_z-r L_y\right) q_3 & \left(p L_y-q L_x\right) q_2+2 L_z \left(q q_0+p
q_3\right)-2 r \left(L_y q_0+L_x q_3\right) & \left(q L_z-r L_y\right) q_1+\left(r L_x-p L_z\right) q_2 \\
\end{array}
\right]^T
\end{align}
\end{subequations}