Chaotic vessel motions and capsize in beam seas

This thesis employs analytic, numeric, and experimental methods to study multiple degree of freedom vessel capsize in beam seas. It begins by improving upon the quasi-nonlinear capsize simulator initially developed by Young-Woo Lee and employs this simulation tool to study the effects of initial conditions on the ultimate state of the vessel following a similar methodology to that developed by Thompson and coauthors for a single degree of freedom system in the early 1990's. In order to yield a practical tool for real world applications this numerical methodology is combined with a probabilistic model to offer a new approach to anticipating and regulating vessel stability. Lastly, previous marine applications of Lyapunov exponents are furthered through comparison of exponents calculated from numerical and experimental time series to demonstrate the usefulness of such a process as a validation tool for simulation. The Lyapunov exponent is a measure of the sensitivity of the system to initial conditions. A positive Lyapunov exponent indicates chaos, defined herein as exponential divergence of nearby trajectories. Short time Lyapunov exponents (similar in definition to local Lyapunov exponents) are used to demonstrate and indicate chaotic behavior on a finite time scale with applications to non-infinite vessel processes such as those leading to capsize. A predictor-corrector methodology for calculating short time Lyapunov exponents from experimental time series using numerical simulation to provide an expression for the Jacobian of the system is developed and discussed.