Motion transitions of falling plates via quasisteady aerodynamics

In this paper, we study the dynamics of freely falling plates based on the Kirchhoff equation and the quasisteady aerodynamic model. Motion transitions among fluttering, tumbling along a cusp-like trajectory, irregular, and tumbling along a straight trajectory are obtained by solving the dynamical equations. Phase diagrams spanning between the nondimensional moment of inertia and aerodynamic coefficients or aspect ratio are built to identify regimes for these falling styles. We also investigate the stability of fixed points and bifurcation scenarios. It is found that the transitions are all heteroclinic bifurcations and the influence of the fixed-point stability is local.