Abstract
Butterfly's flight attracts us in terms of flapping-flight mechanism, in which separation vortices generated by flapping wing play an essential role. In this paper, mathematical analysis of such flapping flight are presented. Simplified flapping models of free-flight are numerically analyzed in terms of the bifurcation structure of the flight states, which provides us with an insight of the nature of vortex- using flight. Theoretical analysis of vortex-using flapping flight are also introduced. The theory is constructed based on the generalized Blasius formulae, which enable us to calculate the force acting on insects only by the far-field information.
