classical mechanics - Lagrangian of the Euler equations

Do the Euler equations (where $I_1,I_2,I_3$ are principal moments of inertia):

$$I_1\dot{\omega}_1+(I_3-I_2)\omega_2\omega_3=M_1$$ $$I_2\dot{\omega}_2+(I_1-I_3)\omega_3\omega_1=M_2$$ $$I_3\dot{\omega}_3+(I_2-I_1)\omega_1\omega_2=M_3$$

in their above general form have a Lagrangian? If not, does a specific case of $\omega_1=\omega_2=0$ (and so $M_1=M_2=0$) have a general Lagrangian? ($M_3$ is the torque coming from a central gravitational potential - a planet - keeping the body (a satellite) on an elliptic orbit.)