Using wind tunnel tests, insect flight dynamics can be studied in a very similar fashion to that of man-made aircraft. Linearized longitudinal flight equations for a bumblebee have been found in the unforced case to be

where u= forward velocity; w= vertical velocity, q= angular pitch rate at center of mass, and θ = pitch angle between the flight direction and the horizontal (Sun, 2005).

a. Use MATLAB to obtain the system’s eigenvalues.

b. Write the general form of the state-transition matrix. How many constants would have to be found?

-8.792 x 10-3 0.56x 10-3 -1.0x 10-3 -13.79 x 10-3 -0.347 x 10-3 -11.7 x 10-3 -0.347 x 10-3 0.261 -20.8 x 10-3 -96.6 x 10-3 1