On Unstable Ship Motions Resulting From Nonlinear Coupling

Abstract

Nonlinear equations of motion of a ship having the three degrees of freedom of heave, pitch, and roll are investigated. The nonlinear terms are all of second order; they represent couplings between the degrees of freedom and, if they were ignored, coupling between some of the equations would be eliminated. It is shown that unstable motion may occur in any one of the degrees of freedom through excitation by one of the other two. Instabilities occur when the natural frequency in the unstable motion is nearly one half of that of the exciting motion, or when these natural frequencies are nearly equal. Experiments have been carried out for the roll-heave systems, and these have confirmed the analysis.