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We study a possible correspondence between the softening of the wobbling modeand the "phase transition" of the one-dimensionally rotating mean field to athree-dimensionally rotating one by comparing the properties of the wobblingmode obtained by the one-dimensional cranking model + random phaseapproximation with the total routhian surface obtained by the three-dimensionaltilted-axis cranking model. The potential surface for the observed wobblingmode excited on the triaxial superdeformed states in $^{163}$Lu is alsoanalyzed.Comment: 13 pages, 6 figures, Phys. Rev. C, accepte

Instability of nuclear wobbling motion and tilted axis rotation