Phase space analysis of roll dynamics and stability for a semisubmersible near neutral equilibrium

Determining the vertical centre of gravity (KG) of in-service semisubmersibles via conventional inclining tests is economically prohibitive. The alternative Zero GM method addresses this by transiently inducing a slightly negative metacentric height (GM) to identify the neutral equilibrium point (KG = KM), raising critical questions about dynamic safety. This paper presents an integrated experimental and numerical investigation of roll dynamics near this bifurcation. Model tests and nonlinear analysis for three KG conditions reveal that the drastically reduced natural roll frequency shifts the response dominance to low-frequency drift forces. Spectral analysis confirms this transition, while phase space analysis provides the fundamental safety explanation. The computed homoclinic and heteroclinic orbits define the boundaries of safe motion. Results demonstrate that large-amplitude “slow jumps” between loll angles, while crossing inner homoclinic basins, remain entirely bounded by the outer heteroclinic manifold. Consequently, capsizing did not occur. This work proves that safety near neutral equilibrium is governed by the global topology of phase space, not merely the GM sign, providing a rigorous, physics-based validation of the Zero GM method and advancing performance-based stability assessment.