A hybrid system consisting of a rotating rigid hub and a flexible appendage following the Timoshenko beam assumptions where shear deformations are taken into account is introduced. Generalization of Lagrange's equations utilizing Hamilton's extended principle is used to derive the equations of motion and the boundary conditions of the system. Applying the Laplace transform to the integro-partial equations of motion leads to a generalized state space model for the frequency domain representation

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... of the system. The beam sub-problem is then solved and utilized for insights for the solution of the full system. Boundary conditions at the beam free end are imposed to obtain the full solution for the state space model. The solution is used to generate transfer functions for both the rigid and the flexible modes of the system in terms of the input torque at the rigid rotating hub. No modal truncation errors are introduced into the transfer function calculations. Numerical results are presented for transfer functions frequency response using the generalized state space solution methodology.