Flight Dynamic Stability of a Flapping Wing Micro Air Vehicle in Hover

This paper discusses a methodology of analyzing the flight dynamic stability of a flapping wing Micro Air Vehicle (MAV) in hover. The flexible flapping wings are modeled by a strain-based geometrically nonlinear beam formulation, coupled with an empirical aerodynamic formulation for load calculation on the wings surfaces. Wing flapping kinematics is described using a set of Euler angles. Nonlinear equations of motion for the body frame attached to the vehicle are used to complete the coupled aeroelastic and flight dynamic formulation. All these formulations are implemented in an integrated numerical framework. To evaluate the flight dynamic stability of the hovering flapping wing MAV, the coupled nonlinear governing equations are linearized, and the transition matrix over a wing flapping cycle is determined. By taking advantage of the periodic hovering condition, the stability analysis is performed based on the transition matrix in the Floquet theory. Longitudinal and lateral stabilities of a flapping wing MAV in hover is explored with the impact of different wing rigidity and inertia.