Euler's Equations of Motion for Rotation of Rigid Body/Also presented as

Euler's Equations of Motion for Rotation of Rigid Body: Also known as

$\ds I_1 \dfrac {\partial \omega_1} {\partial t} - \paren {I_2 - I_3} \omega_2 \omega_3$

$=$

$\ds M_1$

$\ds I_2 \dfrac {\partial \omega_2} {\partial t} - \paren {I_3 - I_1} \omega_3 \omega_1$

$=$

$\ds M_2$

$\ds I_3 \dfrac {\partial \omega_3} {\partial t} - \paren {I_1 - I_2} \omega_1 \omega_2$

$=$

$\ds M_3$

where:

$I_1$, $I_2$ and $I_1$ are the components of the torque applied about the principal axes

$I_1$, $I_2$ and $I_1$ are the moments of inertia at fixed point $O$

$\omega_1$, $\omega_2$ and $\omega_3$ are the components of angular velocity along the principal axis.