Abstract: The strict complementary extremum-saddle point theorem for two prob-lems of new nonlinear form are obtained,and the generality and effectiveness for secondvariation-convex analysis method suggested are demonstrated in this paper.The first prob-lem is rotating tubro impeller,and by introducing the periodic free surface variable we obtainall complementary variational principles.The second problem is non K-L shell with rotaryvaridfble having specific nonlinear geometrical property,and we establish the comple...