In this paper a new approach in the global transient analysis of nonlinear systems is presented; it has the advantages of being conceptually simpler and at the same time more relevant than one based soley on a stability analysis of the steady-state motions. We address the problem of analysing the global transient stability of nonlinear systems in terms of basins of attraction. We show that at a forcing level that is considerably smaller than that at which the steady state attractor loses its stability, there may exist a rapid erosion and stratification of the basin, signifying a global loss of engineering integrity of the system. This conclusion is reinforced by the fact that basin boundaries can become fractal, resulting in chaotic transients, adding a new degree of uncertainty in the response.
The techniques developed are then applied to a ship roll model with cubic and quintic nonlinearities as well as linear plus cubic damping characteristics.