Two variational principle(VP)families for fully 3-D transonic potential-, Beltramiand rotational flows with shocks in a rotor are put forth in terms of stream functions, being a continuation and further development of Ref. [1]. By means of functional variations with variable domain one succeeded in converting most of the boundary conditios and the matching conditions across unknown discontinuities (Such as shocks and free trailing vortex sheets), including the generalized Rankine-Hugoniot shock relations, into natural ones. This paper is intended to provide a rigorous theoretical basis for constructing a novel computational method, which, incorporating a new finite element with self-adapting embedded discontinuities (now under development) and the artificial density concept, might figure out all unknown discontinuities automatically and clearly. The applicability of the VP: for rotational flow, in contrast to those for Beltrami flow, is not confined to transonic flow with moderate Mach numbers. All the VP: presented herein can be extended to hybrid problems in the way similar to that used ref.[26].