Passive Dynamic Stability of a Hovering Fruit Fly: a Comparison between Linear and Nonlinear Methods

抄録

Insects exhibit exquisite control of their flapping flight, capable of performing precise stability and steering maneuverability. To tackle this highly nonlinear problem we have developed two simulation-based methods to investigate the dynamic passive stability of insect flight: linear and nonlinear methods. In the linear theory, the equations of body motion are linearized and the techniques of eigenvalue and eigenvector analysis are employed to obtain the natural modes. Three natural modes are identified including an unstable oscillatory mode, a stable fast subsidence mode and a stable slow subsidence mode, which indicate that the fruit fly hovering flight is dynamic unstable. While in the nonlinear theory, the equations of 6 DoF motion are solved directly by coupling with the N-S equations. The time-varying time histories of the state variables are calculated, indicating that the state of fruit fly under disturbance conditions shows a very nonlinear transient interval initially but turns to unstable eventually. However, our results also illustrate that a fruit fly does have sufficient time to apply some active mediation to sustain a steady hovering before losing body attitudes.