Abstract
The concepts of Maclaurin’s and Taylor’s series expansions of conventional mathematics are adapted to the general time dependent Volterra functional series. Examples of the resulting technique are discussed in relationship to the behaviour of a ship model undergoing steady tow and planar motion mechanism (PMM) oscillatory experiments. The analysis is extended to include the description of the fluid forces acting on a ship model excited in small perturbations about an existing large parasitic motion. It is shown that a linear approximation to the description of the fluid action can again be found and the theory is used to develop a general analysis permitting more sophisticated model experiments to be undertaken and providing a rational means of interpreting experimental measurements taken when a model is oscillated in waves. The analysis is extended to a model which performs a parasitic motion about a mean position fixed in a wave.
Finally the analysis is extended to include the general description of a fluid action dependent on several large parasitic motions as may occur when a ship is excited in a seaway. This general theory may be used for both deterministic and random motions.
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