On the Motion of Solids Through an Ideal Liquid: Approximated Equations for Many Body Systems

Abstract

The problem of motion of many solids through an unbounded ideal liquid (inviscid and irrotational) is considered. A Lagrangian formulation of the equations of motion leads to a set of ordinary differential equations (ODEs) coupled to an elliptic partial differential equation (PDE) [H. Lamb, Hydrodynamics, 6th ed., Dover, New York, 1932]. Here, using a variational approach, an approximated solution for the PDE is presented, and the problem is reduced to the study of a system of ODEs. As a consequence one can get approximate forces and torques due to hydrodynamic interaction of rigid bodies of arbitrary shapes. Some examples are discussed at the end.