Euler's equations

Putting these in (A), we get

These equations are known as Euler's equations named after a swiss mathematician. The conditions under which these equations are applicable are as follows:

(1) The reference point where the body axes are fixed is a point fixed in space or is the center of mass itself. It can also be a point accelerating towards or away from the center of mass.

(2) The xyz reference frame is fixed on the body and is directed along the principal axes at the reference point.

(3) The moments of the forces are taken about the reference point and also the components of the inertia matrix are determined with respect to the body axes at that point.