Damping coefficients for extreme rolling and capsize: An analytical approach

A method to identify the law of roll motion decay from extreme angles is pr esented based on perturbations of the elliptic-type solutions of the corres ponding Hamiltonian system. Restoring polynomials up to the 7th order are c onsidered. It is shown that the decay law can be expressed in closed form f or up to quintic restoring. The method should be especially useful for deri ving linear and nonlinear roll damping coefficients in the context of ship capsize investigations where the large amplitude behavior, near to the angl e of vanishing stability. needs to be taken into account.