Dynamic flight stability of a hovering model insect:lateral motion

The lateral dynamic flight stability of a hovering model insect(dronefly) was studied using the method of computational fluid dynamics to compute the stability derivatives and the techniques of eigenvalue and eigenvector analysis for solving the equations of motion.The main results are as following. (i) Three natural modes of motion were identified: one unstable slow divergence mode(mode 1),one stable slow oscillatory mode(mode 2),and one stable fast subsidence mode(mode 3).Modes 1 and 2 mainly consist of a rotation about the horizontal longitudinal axis(x-axis) and a side translation;mode 3 mainly consists of a rotation about the x-axis and a rotation about the vertical axis,(ii) Approximate analytical expressions of the eigenvalues are derived, which give physical insight into the genesis of the natural modes of motion.(iii) For the unstable divergence mode,t, the time for initial disturbances to double,is about 9 times the wingbeat period(the longitudinal motion of the model insect was shown to be also unstable and tof the longitudinal unstable mode is about 14 times the wingbeat period). Thus,although the flight is not dynamically stable,the instability does not grow very fast and the insect has enough time to control its wing motion to suppress the disturbances.