Title: A Floating Cylinder on An Unbounded Bath,
Abstract: In this paper, we reconsider a circular cylinder horizontally floating on an
unbounded reservoir in a gravitational field directed downwards, which was
studied by Bhatnargar and Finn in 2006. We follow their approach but with some
modifications. We establish the relation between the total energy relative to
the undisturbed state and the total force. There is a monotone relation between
the height of the centre and the wetting angle. We study the number of
equilibria, the floating configurations and their stability for all parameter
values. We find that the system admits at most two equilibrium points for
arbitrary contact angle, the one with smaller wetting angle is stable and the
one with larger wetting angle is unstable. The initial model has a limitation
that the fluid interfaces may intersect. We show that the stable equilibrium
point never lies in the intersection region, while the unstable equilibrium
point may lie in the intersection region.