An Apparent Conservation's Laws Inconsistency Associated With Mixed Added--Mass Coefficients

The examination whether the conservation laws are violated due to the added mass matrix provided here. This work points to inconsistency of the momentum and mass conservation which might also indicate issues with energy conservation in the added mass matrix. In doing so the author invites all to check these inconsistency of the conservation laws. The purpose of this work is not to dismiss the substantial achievements of the added–mass matrix formulation. The theories developed by Kirchhoff, Lamb, Landweber, Newman, Faltinsen, Fossen, and their successors have provided valuable insights and have proven useful in many practical applications. Their success in naval architecture, maneuvering prediction, and fluid–structure in-teraction is undeniable. Nevertheless, the usefulness of a theory does not exempt it from examination. The present work does not claimthat all previous results are incorrect, nor does it deny the practical value of the existing formulations. Rather, it raisesa specific question concerning the consistency of certain mixed added–mass terms with the fundamental conserva-tion laws of mechanics. If the argument presented herein is correct, then the apparent contradiction should not be interpreted as evi-dence for a new source of energy. Instead, it should be viewed as an indication that some assumption, interpretation, or limitation of the traditional formulation has not yetbeen fully understood. The author therefore presents these observations in the spirit of inquiry rather than confrontation. The objectiveis not to replace a successful theory, but to identify and resolve an apparent inconsistency so that the theory may beunderstood on a firmer foundation. Throughout this investigation, the author has attempted to approach the subject with humility and caution. The added–mass framework has served the engineering community well for many decades, and any claim of inconsistency must therefore be held to a high standard of evidence. At the same time, progress in science requires that apparent contradictions be examined rather than ignored. The goal of the present work is simply to determine whether the observed energy imbalance reflects an error in the analysis, an overlooked assumption, or a genuine limitation of the current formulation.