Ship stability criteria based on chaotic transients from incursive fractals

TLDR

This article surveys recent nonlinear dynamics of driven oscillators that suggest a new way to quantify ship stability in waves. It is argued that the observed basin erosion could serve as a basis for a design criterion grounded in transient motions. The study finds that when resonant motions can escape over a potential energy peak, the safe basin of attraction abruptly shrinks, producing a gross striation and occurring at forcing levels far below those that destabilize steady‑state motions, thereby offering a conceptually simpler and more relevant design criterion than traditional steady‑state stability analyses.

Abstract

This article surveys some recent findings in the nonlinear dynamics of driven oscillators that appear to offer a new approach to the quantification of ship stability in waves. The major discovery is that in situations where the resonant motions can escape over a local maximum of the potential energy (as in capsize), there is always likely to be a sudden reduction in area of the safe basin of attraction in the space of the starting conditions. This is associated with a gross striation of the basin, and can occur at a forcing magnitude that is a small fraction of that at which the final steadystate motions lose their stability. It is argued that this well-defined basin erosion could form the basis of a new design criterion based on transient motions. This approach has the twin advantages of being both conceptually simpler and at the same time more relevant than one based on a stability analysis of the steady state rolling motions which can be dangerously non-conservative.