The challenges of providing safe and high performance marine vehicles present strict and often conflicting constraints that require rational and holistic analysis methodologies to obtain efficient design solutions. This paper presents a mathematical framework for stability analysis, which is one of the key elements in the design and operation of ships and floating bodies that still require considerable improvement. The method is based on the application of the Lyapunov stability analysis concept, which has been highly successful in some other engineering and scientific disciplines. The paper presents the fundamental concepts on the applicability of the Lyapunov method to ship motions stability analysis. Governing mathematical models are derived from first principles and interpreted in the context of geometrical and physical interrelationships. The analytical models are primarily developed for the generalized case of non-linear forced non-conservative systems and simplified by linearization in the case of coupled motion for detailed analysis and characterization of stability conditions and domain. The concept of “motion boundedness” is introduced to satisfy requirements of the Lyapunov method to ship motions subjected to continuous excitations. The analysis leads to some valuable deductions and insight that would be useful in the formulation of stability criteria for ships and marine vehicles in general. The most significant contribution is the possibility of explicit determination of geometric and hydrostatics/hydrodynamics parameters that govern ship stability characteristics.
VARIATIONAL LYAPUNOV METHOD AND STABILITY ANALYSIS FOR PERTURBED SETVALUED IMPULSIVE INTEGRO-DIFFERENTIAL EQUATIONS WITH DELAY
