title: The need for higher-order averaging in the stability analysis of hovering, flapping-wing flight.
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.
authors.affiliation: University of California, Irvine, CA, USA.
authors.forename: Haithem E
authors.initials: HE
authors.lastname: Taha
authors.forename: Sevak
authors.initials: S
authors.lastname: Tahmasian
authors.forename: Craig A
authors.initials: CA
authors.lastname: Woolsey
authors.forename: Ali H
authors.initials: AH
authors.lastname: Nayfeh
authors.forename: Muhammad R
authors.initials: MR
authors.lastname: Hajj
mesh_terms: D000818:Animals; D001683:Biological Clocks / Q000502:physiology*; D003198:Computer Simulation; D005426:Flight, Animal / Q000502:physiology*; D007313:Insecta / Q000502:physiology*; D016014:Linear Models; D008954:Models, Biological; D009949:Orientation / Q000502:physiology; D009991:Oscillometry / Q000379:methods; D012212:Rheology / Q000379:methods*; D014921:Wings, Animal / Q000502:physiology*