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Use the analogy of the 'cone' lying on its side.
This a mechanically 'Neutral Equilibrium'.
Not 'Stable' (self correcting) Disturbance => Return to Initial
Condition.
Nor 'Unstable' Disturbance => disaster
But' Neutral'
Disturbance => moves to (most likely) New, Different condition of
equilibrium.
Circles and ellipses are both neutral equilibrium conditions.
Each disturbance shifts the system to different (but still neutrally
stable) equilibrium.
Confusion comes from naming the 'cone standing upright' as Stable
while naming the lying down on its side as being 'Neutrally Stable'
Perhaps we need a pedagogical adjective to describe the 'Standing
Upright' stability as maybe 'Self-Correcting Stability'
as opposed to
'Go-with-the-Flow (neutral) Stability.
I think that PC (Pedagogically Correct) semantics
is a big part of this current discussion.