Recently, I was reading about stability of equilibrium. I came across the definitions for different types of equilibrium.
Neutral Equilibrium: The kind of equilibrium of a body so placed that when moved slightly it neither tends to return to its former position not depart more widely from it.
Unstable Equilibrium: A kind of equilibrium in which, if the system is displaced an arbitrarily small distance from the equilibrium state, the forces of the system cause it to move even farther away.
Stable Equilibrium: A kind of equilibrium in which, if the system is displaced an arbitrarily small distance from the equilibrium state, the forces of the system cause it to move back to the original equilibrium position.
In all the books and resources which I came across, these equilibrium were analyzed only for 1 dimension. So I was thinking what will be the case in 3 Dimension if along all the three orthogonal directions we had different equilibrium.
When I asked my teacher he said in order for a system to be in stable equilibrium it must be so in all the directions possible.
Hence my conclusion was even if in one direction the system was in unstable equilibrium the system in general is in unstable equilibrium.
Then I tried to think what if in all directions the system is in stable equilibrium except a particular direction in which the equilibrium is neutral.
For example, look at the shape above. If we place this rigid structure on the floor and a ball in the middle of this structure we obtain a configuration. Now I am unable to figure out whether the configuration is Stable or Neutral Equilibrium(I'm pretty sure this is not Unstable).
Either way I tried to classify it and I find the classification either way is unsatisfactory and I find no book or website mention this kind of situation.
So my question is, Is this configuration Stable or Neutral?