Averaging of the Nonlinear Dynamics of Flapping Wing Micro Air Vehicles for Symmetrical Flapping

First order equations of motion for a flapping wing micro-air vehicle are presented. The first order, longitudinal equations of motion are obtained from the second-order, strongly coupled, multi-body equations of motion using an approximate inverse. The nonlinear dynamics of the longitudinal equations of motion are averaged using two different methods: local averaging over a fully flapping cycle and local averaging over quarter-flapping cycles. Open loop simulations are presented, near a hover condition, for both averaged systems. The results for the locally averaged system are not consistent with the solution to the full system - suggesting that the neglecting of individual contributions to the dynamics, due to averaging over the entirety of a flapping cycle, is not a valid approach. Better results are obtained when the equations of motion are averaged over a quarter of a flapping cycle. The quarter-cycle results show a significant improvement in the accuracy of the position and orientation of the simulations versus the cycle averaged simulations.

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