When the Poincare map associated with a periodic orbit of a hybrid dynamical system has constant-rank iterates, we demonstrate the existence of a constant-dimensional invariant subsystem near the orbit which attracts all nearby trajectories in finite time. This result shows that the long-term behavior of a hybrid model with a large number of degrees-of-freedom may be governed by a low-dimensional smooth dynamical system. The appearance of such simplified models enables ...
Geckos are nature's elite climbers. Their remarkable climbing feats have been attributed to specialized feet with hairy toes that uncurl and peel in milliseconds. Here, we report that the secret to the gecko s arboreal acrobatics includes an active tail. We examine the tail s role during rapid climbing, aerial descent, and gliding. We show that a gecko s tail functions as an emergency fifth leg to prevent falling during ...
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