Instant Chaos, Extreme Parametric Uncertainty, and Sustained Chaotic Transients in Nonlinear Continuum Mechanics

Bifurcation to high-dimensional hyperchaos is observed in a driven coupled pendulum-flexible rod system. When the rod is in resonance with the pendulum, the system changes from a low dimensional attractor to a high dimensional attractor abruptly. It is shown that high dimensional chaotic dynamics is hysteretic, and exhibits extreme sensitivity with respect to small parameter changes. Such sensitivity poses a problem in obstructing predictability in mechanics. A brief discussion of sustaining chaos to prevent resonance is included.