## Equations of Attitude Motion about mass centre
$
\begin{aligned}
{\bf M}^* = &&{\bf I}^* \cdot \boldsymbol \alpha
+ \boldsymbol \omega \times ({\bf I}^* \cdot \boldsymbol \omega)
+ \frac{^Bd {\bf I}^*}{\mathrm{d}t} \cdot \boldsymbol \omega \\
&&+ \int_{S_0} \rho \mathbf{[p \times (\boldsymbol \omega\times p)](v_r \cdot {n})} \, dS + \int_{V_0} \rho \mathbf{[\boldsymbol \omega \times (p \times v_r)]} \, dV\\
&&+ \int_{V_0} \rho \mathbf{[\boldsymbol \omega \times (p \times v_r)]} \, dV
+ \frac{^Bd}{\mathrm{d}t} \int_{V_0}\rho \mathbf{(p \times v_r)} \, dV\\
&&+ \int_{S_0} \rho \mathbf{(p \times v_r)}(\mathbf{v_r} \cdot {\mathbf n}) \, dS.
\end{aligned}
$