SHORT-DISTANCE ASYMPTOTICS OF THE ADDED-MASS MATRIX OF TWO SPHERES OF EQUAL DIAMETER

A systematic short-distance asymptotic expansion of the added-mass matrix mA is derived. The starting point of the derivation is the classical (essentially long-distance) convergent-series expansion of mA. The series is first converted by an (inverse) Mellin transformation into an integral representation, from which the asymptotic expansion is deduced by a shift of the (complex) contour of integration and by the application of the residue theorem. The optimal approximation of the matrix mA by a finite number of terms of the asymptotic expansion is investigated; it turns out that the optimal approximants contain considerably more terms of the expansion than those available previously from rather tedious computations of other authors. In order to prove optimality one needs even more terms of the asymptotic expansion then those necessary for the optimal approximation. The optimal asymptotic approximants prove useful in a range of one order of magnitude larger than the approximants known previously.