The work objectives are to generalize the scalarization method of dynamic elastic fields in the transversely isotropic media to the tasks for the environments rotating with a constant angular velocity, and to develop the methodological apparatus for describing the effect of rotation on the parameters of surface acoustic waves. On the basis of this method, the scientific-methodical device for the construction of new acoustic-wave gyroscopes is proposed. Parameter determination ratios for surface-acoustic waves (SAW) propagating on the boundary of the rotating half-space of the transversely isotropic material with arbitrarily spaced axis of material symmetry are obtained and validated. An example of the numerical simulation for the isotropic rotating half-space case is given. The proposed methodological apparatus and numerical simulation examples can be used to develop new types of gyroscopes on acoustic-wave systems for navigation, guidance and control of various mobile objects in aviation, robotics, etc