Experimental versus theoretical robustness of rotating solutions in a parametrically excited pendulum: A dynamical integrity perspective

The objective of this paper is showing how global safety arguments can be fruitfully used to interpret experimental results of a pendulum parametrically excited by wave motion. In fact, the results of an experimental campaign developed with the aim of simulating sea-waves energy production by a parametric pendulum show that rotations exist in a region which is smaller than the theoretical one. This discrepancy can be partially attributed to the experimental approximations and constraints, but it has a deeper theoretical motivation. By comparing the experimental results with the dynamical integrity profiles we have found that experimental rotations exist only where a measure of dynamical integrity accounting for both attractor robustness and basin compactness is large enough, so that they can support experimental imperfections leading to changes in initial conditions.