Consider a force acting on a rocket at two angles where the rocket and rotate in three angles shown in the figure below.

Would the global force vectors, that is, the force vectors that are acting on the point (x, y, z) which are paralell to the global coordinate axes be the (x, y, z) values of the point P_3 shown in the diagram below?

I’ve thought about this several times and it should work. Rotating locally means by \alpha and \beta shown in the first figure and globally by the rockets angles.