This dissertation presents novel vibrational control strategies for mechanical control-affine systems with high-frequency, high-amplitude inputs. Since these control systems use high-frequency, zero-mean, periodic inputs, averaging techniques are widely used in the analysis of their dynamics. By studying their time-averaged approximations, new properties of the averaged dynamics of this class of systems are revealed. Using these properties, the problem of input optimization of vibrational control systems was formulated and solved by transforming the problem to a constrained optimization one. Geometric control theory provides powerful tools for studying the control properties of control-affine systems. Using the concepts of vibrational and geometric controls and averaging tools, a closed-loop control strategy for trajectory tracking of a class of underactuated mechanical control-affine systems is developed. In the developed control law, the fact that for underactuated systems, the actuated coordinates together with the corresponding generalized velocities can be considered as generalized inputs for the unactuated dynamics plays the main role. Using the developed control method, both actuated and unactuated coordinates of the system are able to follow slowly time-varying prescribed trajectories on average. The developed control method is applied for altitude control of flapping wing micro-air vehicles by considering the sweeping (flapping) angle of the wings as the inputs. Using the feathering (pitch) angles of the wings as additional inputs, and using non-symmetric flapping, the control method is then extended for three-dimensional flight control of flapping wing micro-air vehicles. / Ph. D.