On the manifestation of coexisting nontrivial equilibria leading to potential well escapes in an inhomogeneous floating body

• Published in: Physica. D Vol. 365; pp. 80 - 90
• Main Authors: Sequeira, Dane, Wang, Xue-She, Mann, B.P.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.02.2018
• Subjects: Bifurcation; Coexisting solutions; Potential well escape; Bifurcation; Coexisting solutions; Potential well escape
• ISSN: 0167-2789; 1872-8022
• DOI: 10.1016/j.physd.2017.11.002

This paper examines the bifurcation and stability behavior of inhomogeneous floating bodies, specifically a rectangular prism with asymmetric mass distribution. A nonlinear model is developed to determine the stability of the upright and tilted equilibrium positions as a function of the vertical position of the center of mass within the prism. These equilibria positions are defined by an angle of rotation and a vertical position where rotational motion is restricted to a two dimensional plane. Numerical investigations are conducted using path-following continuation methods to determine equilibria solutions and evaluate stability. Bifurcation diagrams and basins of attraction that illustrate the stability of the equilibrium positions as a function of the vertical position of the center of mass within the prism are generated. These results reveal complex stability behavior with many coexisting solutions. Static experiments are conducted to validate equilibria orientations against numerical predictions with results showing good agreement. Dynamic experiments that examine potential well hopping behavior in a waveflume for various wave conditions are also conducted. •Stability analysis is presented for an inhomogeneous floating body.•Bifurcation diagrams and basins of attraction reveal complex stability behavior.•Static experiments are conducted to verify numerical results.•Dynamic experiments are conducted to investigate potential well hopping.