Qualitative Analysis of Non-linear Systems

Project Abstract

Given the fact that qualitative approach to understand the nonlinear behavior of physical systems provides us only a partial understanding of the solution, quantitative analysis is a very crucial step in the analysis of any of the physical systems. It involves drawing key insights and conclusions based on the pre-determined responses, under certain critical conditions. We have considered the analysis of the motion of a ship in irregular seas, which happens to be nonlinear in nature, and focused our efforts on observing the factors that lead to the capsizing of a ship. Out of the six degrees of motion of a ship, the roll motion is observed to be more predominant that any other motion in triggering capsizes. Hence we have considered the ship dynamics in pure roll motion as our criteria for analysis. The analysis is performed by Phase Plane Analysis and the results are compared to those obtained by numerical computation.