A view on capsizing under direct and parametric wave excitation

The behavior of a ship that is simultaneously heaving, swaying and rolling in waves is examined by using an early developed model by Thompson et al. [Thompson, J. M. T., Rainey, R. C. T. and Soliman, M. S. (1992) Mechanics of ship capsize under direct and parametric wave excitation. Philosophical Transactions of the Royal Society London A 338, 471-490]. A second-order nonlinear differential equation has been used as a mathematical model which is analyzed by using numerical methods to obtain geometrical phase space techniques of nonlinear dynamics. Bifurcation diagrams and Poincaré maps are two of the geometrical techniques used in this study. The result of the calculation is given to allow the naval architect to make a self comparison.