The moment equations for oblique wing aircraft are similar to the standard conventional aircraft equations but must be modified due to the cross-products of the aircraft inertia matrix not being zero.
$$\begin{matrix}
L=I_x\dot{p}-I_{yz}(q^2-r^2)-I_{zx}(\dot{r}+pq)-I_{xy}(\dot{q}-rp)-(I_y-I_z)qr \\
M=I_y\dot{q}-I_{yz}(r^2-p^2)-I_{xy}(\dot{p}+qr)-I_{yz}(\dot{r}-pq)-(I_z-I_x)rp \\
N=I_z\dot{r}-I_{xy}(p^2-q^2)-I_{zy}(\dot{q}+rp)-I_{zx}(\dot{p}-qr)-(I_x-I_y)pq
\end{matrix}$$
For the state-space representation, we get
$$\begin{bmatrix}
\dot{p} \\
\dot{q} \\
\dot{r}
\end{bmatrix}=
f_f(\bar{x})+g_f(\bar{x})u=
\begin{bmatrix}
f_p(\bar{x}) \\ f_q(\bar{x}) \\ f_r(\bar{x})
\end{bmatrix}+
\begin{bmatrix}
g_{p_{\delta_{aL}}} & g_{p_{\delta_{aR}}} & g_{p_{\delta_{r}}} &g_{p_{\delta_{eL}}} & g_{p_{\delta_{eR}}} \\
g_{q_{\delta_{aL}}} & g_{q_{\delta_{aR}}} & g_{q_{\delta_{r}}} &g_{q_{\delta_{eL}}} & g_{q_{\delta_{eR}}} \\
g_{r_{\delta_{aL}}} & g_{r_{\delta_{aR}}} & g_{r_{\delta_{r}}} &g_{r_{\delta_{eL}}} & g_{r_{\delta_{eR}}} \\
\end{bmatrix}\cdot
\begin{bmatrix}
\delta_{aL} & \delta_{aR} & \delta_{r} & \delta_{eL} & \delta_{eL}
\end{bmatrix}^T$$
Where the state vector is
$$\bar{x}=
\begin{bmatrix}
p & q & r & \alpha & \beta & \mu & u &\gamma & H
\end{bmatrix}^T$$
- wangDynamicCharacteristicsAnalysis2016
[[6DoF Moment Equations]]
[[Oblique Wing Aircraft]]
[[State-Space Model]]