Equilibrium and Stability

Equilibrium

A system is in equilibrium when:

$$ \frac{dU}{dx} = 0 $$

Stability

To determine stability, examine the second derivative:

• Stable equilibrium:

$$ \frac{d^2 U}{dx^2} > 0 $$

• Unstable equilibrium:

$$ \frac{d^2 U}{dx^2} < 0 $$