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J R Soc Interface. 2013 May 22;10(85):20130269. doi: 10.1098/rsif.2013.0269. Print 2013 Aug 6.

Nonlinear flight dynamics and stability of hovering model insects.

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Ministry of Education Key Laboratory of Fluid Mechanics, Beijing University of Aeronautics and Astronautics, Beijing 100191, People's Republic of China.


Current analyses on insect dynamic flight stability are based on linear theory and limited to small disturbance motions. However, insects' aerial environment is filled with swirling eddies and wind gusts, and large disturbances are common. Here, we numerically solve the equations of motion coupled with the Navier-Stokes equations to simulate the large disturbance motions and analyse the nonlinear flight dynamics of hovering model insects. We consider two representative model insects, a model hawkmoth (large size, low wingbeat frequency) and a model dronefly (small size, high wingbeat frequency). For small and large initial disturbances, the disturbance motion grows with time, and the insects tumble and never return to the equilibrium state; the hovering flight is inherently (passively) unstable. The instability is caused by a pitch moment produced by forward/backward motion and/or a roll moment produced by side motion of the insect.


equations of motion; flight dynamics; insect; nonlinear stability; the Navier–Stokes equations

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