On two descriptions for many moving bodies through inviscid fluid

Abstract The Lagrangian energy description of multiple rigid bodies moving through an inviscid fluid is proved equivalent to the corresponding momentum-type one using the harmonic function theory. In two dimensional cases, the description can be used to derive the extended unsteady Blasius formulae in the complex form. It indicates that the pressure distribution over the surface of any submerged body are functions of coupled translational and angular accelerations of all bodies, and therefore masses of all bodies influence hydrodynamic loads on a body.