The analytical method uses the curves of the path and profile you specify for the revolution or extrusion and uses the curves to define the revolution or extrusion. Unlike the
Non-analytical Method, for a revolution, it maintains the relationship of the profile and axis. When you edit the revolution or extrusion, you edit the curves making up the object, not the individual points of the profile as you do for non-analytical.
Comparision of revolutions created with analytical and non-analytical methods
Comparision of extrusions created with analytical and non-analytical methods