Equilibrium, Stability, and Dynamics of Rectangular Liquid-Filled Vessels

Abstract

Here we focus on the stability and dynamic characteristics of a rectangular, liquid-filled vessel. The position vector of the center of gravity of the liquid volume is derived and used to express the equilibrium angles of the vessel. Analysis of the potential function determines the stability of these equilibria, and bifurcation diagrams are constructed to demonstrate the co-existence of several equilibrium configurations of the vessel. To validate the results, a vessel of rectangular cross section was built. The results of the experiments agree well with the theoretical predictions of stability. The dynamics of the unforced and forced systems with a threshold constraint is discussed in the context of the nonlinear Mathieu equation.