床を転がるコイン

\begin{align*} \big( I_X + Ma^2 \big) \left({ d\omega_X\over d t} \textcolor{red}{+\alpha|\dot\psi|\omega_X}\right) & = - \big( I_Z +Ma^2\big) \omega_Y\omega_Z {-}I_X \omega_Y^2 \tan {\theta} {+} Ma^2 {g\over a} \sin {\theta} \\%-------------- I_X \left( { d\omega_Y\over d t} \textcolor{red}{+\alpha|\dot\psi|\omega_Y}\right) & = {+}I_X\omega_X \omega_Y\tan {\theta} + I_Z\omega_Z \omega_X \\%-------------- \big( I_Z + Ma^2 \big)\left( { d\omega_Z\over d t} \textcolor{red}{+\alpha|\dot\psi|\omega_Z}\right) & = + Ma^2 \omega_X \omega_Y \\%------------------------------ {d\theta\over dt} & = \omega_X \\ {d\phi\over dt} & = {1\over\cos\theta}\,\omega_Y \\ {d\psi\over dt} & = \omega_Z + \tan\theta\,\omega_Y \end{align*}