L33 : Euler's equations

It has already been stated that rate of change of linear momentum of a body is equal to the net applied force,i.e.,

Similarly, the rate of change of angular momentum is equal to net applied moment, when the terms are taken either about a fixed point O or about the mass center, i.e.,

This equation is valid if the angular momentum H and moment M both are taken about fixed point O or mass center or a point which is moving towards or away from the center of mass.

When H is expressed in terms of components measured relative to a moving coordinatre system, can be written as,