Dynamics of many bodies in a liquid: Added-mass tensor of compounded bodies and systems with a fast oscillating body

An explicit set of ordinary differential equations that approximately describe the dynamics of many rigid bodies (without any hypothesis on their geometry) inside an ideal fluid is presented. Two applications of these equations are made. At first, it is shown how to use these equations to compute the added-mass tensor of a single body made up of simpler units (like spheres, cylinders, and ellipsoids). Then the hydrodynamic force and torque that a small-amplitude fast oscillating body induces on another body that can freely move in its vicinity is computed. The noticeable result is that if the free body is sufficiently far from the oscillating one then the averaged interaction force is attractive if and only if the density of the free body is larger than the density of the fluid. Finally, computations for a pendulum system are presented. It seems that the latter system is suitable for experimentation. (C) 2002 American Institute of Physics.