Euler's equations

In the above set of equations, the following 3 equations for the motion of center of mass are added to make a complete set of equations for the motion of the body:

Examples:

(1) Suppose a body is rotating about x-axis only, then

This mean that if the body is rotating within a constant angular velocity, no net moments act on it.

(2) If the body has the component of angular velocity along x and y axes, then