Static stability analysis of a floating rectangular prism
This paper examines the static stability of a floating rectangular prism. A nonlinear model is developed to determine the stability of the upright and tilted equilibria positions as a function of the vertical location of the prism's center of mass. 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 are generated that illustrate the stability of the equilibrium positions as a function of the vertical location of the center of mass. The bifurcation diagrams show complex stability behavior with many coexisting solutions.
