Relation between Integral Representations and Multipole Expansions (Series Representations) of Velocity Potentials in Ship Motion Theory : the 2nd Report : 3D Problem (with Forward Speed)

Abstract

Succeeding to the first report the present paper gives the mathematical proof the equality of the integral representations to the multipole expansions (series representations) of the velocity potentials in ship motion theory in the case of 3D problems (with forward speed). The coefficients of the series are represented in terms of the source distributions in the integral representation. In order to show the usefulness of the series representations some applications of them to ship motion problems are discussed.