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

TLDR

Dynamic stability analysis of hovering insects and FWMAVs usually relies on direct averaging over a flapping cycle, but this approach can yield misleading conclusions due to the high flapping frequency. The study investigates whether higher‑order averaging is required to accurately capture the dynamics and stability of flapping‑wing flight, comparing direct averaging with second‑order methods. The authors apply second‑order averaging to the hovering dynamics of five insects subjected to high‑amplitude, high‑frequency wing motion, and evaluate its performance relative to direct averaging.

Abstract

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.