Potential well metamorphosis of a pivoting fluid-filled container

Abstract

This paper investigates the stability of a pivoting cylindrical container that is slowly filled with fluid. The action of filling the container with fluid causes the system’s potential energy to evolve and modify the stability of equilibria. We analyze the stability behavior of this system and find distinct regions where edge and spill conditions require alternative expressions for the system’s potential energy. The stability of the upright and tilt angle equilibria are studied using the Lagrange–Dirichlet theorem. We provide exact expressions for the potential energy of the system and bifurcation diagrams that compactly represent the stability behavior of the upright equilibria and additionally predict the presence of non-trivial or tilted equilibria. Theoretical investigations are then compared with a series of experimental tests that validate the container upright and tilted equilibria stability.