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This paper discusses the wing inertial effects on stability of pitch motionof hovering insects. The paper also presents a dynamic model appropriate forusing averaging techniques and discusses the pitch stability results derivedfrom the model. The model is used to predict the body angle of five insectspecies during hover, which are in good agreement with the availableexperimental results from different literature. The results suggest that thewing inertia forces have a considerable effect on pitch dynamics of insectflight and should not be ignored in dynamic analysis of hovering insects. Theresults also suggest that, though the pitch stability of hovering insects isopen-loop stable, it may not be vibrationally stabilized. Instead, the pitchstability is a balance of the moment of insect's weight and the aerodynamicmoment due to flapping kinematics with a nonzero mean stroke angle. Experimentswith a flapping wing device confirm this results. To clearly explain the usedmodel and clarify the difference between vibrational and non-vibrationalstabilization, first this paper discusses the vibrational control of athree-degree-of-freedom force-input pendulum with its pivot moving in avertical plane.

The effects of wing inertial forces and mean stroke angle on the pitch stability of hovering insects