The objective of the present work was to develop an approximation to the conventional mixed linear-plusquadraticship roll damping model so that analytical obstacles could be overcome in the application of the functional series expansion to nonlinear ship rolling. A mixed linear-plus-cubic approximation was found to be reasonable for this purpose. In the course of analyses, there were indications that this model may be closer to an "equivalent approach" than to an "approximation."
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J F Dalzell (1978) studied this question.