In plant cells the terms isotonic, hypotonic and hypertonic can not strictly be used accurately because the pressure exerted by the cell wall significantly affects the osmotic equilibrium point.
The summary of the results is that the three-dimensional homogeneous convex (mono-monostatic) body, which has one stable and one unstable equilibrium point, does exist and is not unique.
This approach typically relies on concavity and differentiability assumptions to track the local evolution of an equilibrium point that varies smoothly with exogenous parameters.
As time progresses, the object sliding slows and the distance it travels during these oscillations becomes smaller until it reaches zero, the equilibrium point.