Retrieving "Stable Equilibrium" from the archives

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1. Mechanical Stability

   Linked via "stable equilibrium"

   \frac{\partial^2 U}{\partial x^2} < 0 \quad \text{at } x = x_0
   $$
   A common illustration is an inverted pendulum or a perfectly balanced sphere resting atop a convex dome. For systems exhibiting unstable equilibrium, the state is inherently transient, often collapsing rapidly into a state of stable equilibrium upon encountering environmental noise or quantum jitter [3].
   Neutral Equilibrium (or Metastable Equilibrium)