Flying snakes, attracting manifolds, and the trajectory divergence rate

Inspired by the gliding behavior of the paradise tree snake, Chrysopelea paradisi, I will discuss a simplified model for passive aerodynamic flight which gives an intuitive and dynamically rich 2 degree-of-freedom system. Within this model, all trajectories collapse quickly onto an attracting codimension-1 manifold in velocity space: the terminal velocity manifold. This curve provides geometric insights into the possible dynamics of passively descending bodies such as gliding animals or falling leaves. As a tool to calculate and understand structures like the terminal velocity manifold, I introduce a scalar quantity, the trajectory divergence rate, which rapidly approximates attracting invariant manifolds based on an instantaneous vector field. This diagnostic may be applied to approximate a variety of structures including slow manifolds and hyperbolic Lagrangian coherent structures.