Modeling of Ship Roll Dynamics and Its Coupling with Heave and Pitch
In order to study the dynamic behavior of ships navigating in severe environmental conditions it is imperative to develop their governing equations of motion taking into account the inherent nonlinearity of large-amplitude ship motion. The purpose of this paper is to present the coupled nonlinear equations of motion in heave, roll, and pitch based on physical grounds. The ingredients of the formulation are comprised of three main components. These are the inertia forces and moments, restoring forces and moments, and damping forces and moments with an emphasis to the roll damping moment. In the formulation of the restoring forces and moments, the influence of large-amplitude ship motions will be considered together with ocean wave loads. The special cases of coupled roll-pitch and purely roll equations of motion are obtained from the general formulation. The paper includes an assessment of roll stochastic stability and probabilistic approaches used to estimate the probability of capsizing and parameter identification.
Coupled Nonlinear Barge Motions: Part I — Deterministic Models Development, Identification and Calibration
This paper focuses on the development of optimal deterministic, nonlinearly coupled barge motion models, identification of their system parameters and calibration of their prediction capability using experimental results. The ultimate objective is to develop accurate yet sufficiently low degree-of-freedom stochastic models suitable for efficient probabilistic stability and reliability analyses of US Naval barges for preliminary design and operation guideline development (see Part II). First a three-degree-of-freedom (3DOF) fully coupled Roll-Heave-Sway model, which features realistic and practical high-degree polynomial approximations of rigid body motion relations, hydrostatic and hydrodynamic force-moment specifically suitable for barges, is examined. The hydrostatic force-moment relationship includes effects of the barge’s sharp edge and combined roll-heave states, and the hydrodynamic force-moment specifically suitable for barges, is examined. The hydrostatic force-moment relationship includes effects of the barge’s sharp edge and combined roll-heave state, and the hydrodynamic terms are in a “Morison” type quadratic form. System parameters of the 3DOF model are identified using physical model test results from several regular wave cases. The predictive capability of the model is then calibrated using results from a random wave test case. Recognizing the negligible sway influence on coupled roll and heave motions and overall barge stability, and in an attempt to reduce anticipated stochastic computational efforts in stability analysis, a 2DOF Roll-Heave model is derived by uncoupling sway from the roll-heave governing equations of motion. Time domain simulations are conducted using the (3DOF) Roll-Heave-Sway and the (2DOF) Roll-Heave models for regular and random wave cases to validate the model assumptions and to assess their (numerical) prediction capabilities.Copyright © 2004 by ASME
Multi-Dimensional Utility and the Index Number Problem: Jeremy Bentham, J. S. Mill, and Qualitative Hedonism
This article develops an unconventional perspective on the utilitarianism of Bentham and Mill in at least four areas. First, it is shown that both authors conceived of utility as irreducibly multi-dimensional, and that Bentham in particular was very much aware of the ambiguity that multi-dimensionality imposes upon optimal choice under the greatest happiness principle. Secondly, I argue that any attribution of intrinsic worth to any form of human behaviour violates the first principles of Bentham's and Mill's utilitarianism, and that this renders both authors immune to the claim by G. E. Moore that they committed a ‘naturalistic fallacy’. Thirdly, in light of these contentions, I find no flaw in Mill's ‘proof of utility’. Fourthly, I use the notion of intrapersonal utility weights to provide an interpretation of Mill's qualitative hedonism that is entirely consistent with his value monism.