Modelling Chaotic Motion of a Sloshing Liquid in a Horizontally Forced Axisymmetric Container With a Forced Spherical Pendulum

摘要

The motion of a sloshing liquid in a horizontally forced axisymmetric container is modelled by a horizontally forced spherical pendulum. The drawback of this model is that the pendulum can exhibit circular motion where the pendulum goes full circle and this has no analogy for the sloshing liquid problem. Thus, different ways of modifying the pendulum equations are considered which restrict the motion of the pendulum. The modified equations have a reflectional symmetry and both symmetric and non-symmetric solutions of these equations are investigated and the transitions between them. In particular, a catastrophic blowout bifurcation is found at which a planar chaotic attractor which is normally stable, undergoes a crisis by colliding with an unstable periodic orbit, resulting in a much larger planar chaotic attractor which is unstable in the normal direction. These results illustrate the type of solutions that might be expected in the full equations for this problem.