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Bioinspir Biomim. 2015 Jan 5;10(1):016002. doi: 10.1088/1748-3190/10/1/016002.

The need for higher-order averaging in the stability analysis of hovering, flapping-wing flight.

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University of California, Irvine, CA, USA.


Because of the relatively high flapping frequency associated with hovering insects and flapping wing micro-air vehicles (FWMAVs), dynamic stability analysis typically involves direct averaging of the time-periodic dynamics over a flapping cycle. However, direct application of the averaging theorem may lead to false conclusions about the dynamics and stability of hovering insects and FWMAVs. Higher-order averaging techniques may be needed to understand the dynamics of flapping wing flight and to analyze its stability. We use second-order averaging to analyze the hovering dynamics of five insects in response to high-amplitude, high-frequency, periodic wing motion. We discuss the applicability of direct averaging versus second-order averaging for these insects.

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