Solvability condition in multi-scale analysis of gyroscopic continua

The solvability condition is investigated for the method of multiple scales applied to gyroscopic continua. The general framework of the multi-scale analysis is proposed for a linear gyroscopic continuous system under small nonlinear time-dependent disturbances. The solvability condition is derived from the properties of the systems. The condition holds only for appropriate boundary conditions. The appropriateness of the boundary conditions can be examined for unperturbed linear systems. An example is presented to highlight the requirements on the boundary conditions.