Geometric Control Approach to Longitudinal Stability of Flapping Flight

Flapping flight dynamics is appropriately represented by a multibody, nonlinear, time-varying system. The two major simplifying assumptions in the analysis of flapping flight stability are neglecting the wing inertial effects and averaging the dynamics over the flapping cycle. The challenges resulting from relaxing these assumptions naturally invoke the geometric control theory as an appropriate analysis tool. In this work, the full equations of motion governing the longitudinal flapping flight dynamics near hover are considered and represented in a geometric control framework. Then, combining tools from geometric control theory and averaging, the full dynamic stability of hovering insects is assessed.