Effects of flexibly torsional wings in flapping-of-wings flight of butterfly

The objective of this paper is to clarify the principle of stabilization in flapping-of-wings flight of a butterfly, which is rhythmic and cyclic motion. For this purpose, a dynamics model of a butterfly is derived by Lagrangepsilas method, where the butterfly is considered as a rigid multi-body system. For the aerodynamic forces, a panel method is applied. Validity of the mathematical models is shown by agreement of the numerical result with the measured data. Then, periodic orbits of flapping-of-wings flights are searched in order to fly the butterfly models. Almost periodic orbits are obtained, but the model in the searched flapping-of-wings flight is unstable. This research, then, studies how the flexibly torsional wings effect on the flight stability. Numerical simulations demonstrate that the flexible torsion reduces the flight instability.