Understanding Equilibrium Stability in Classical Mechanics: Virtual Work Lecture

[gulsen]

In classical mechanics - virtual work lecture, for determining equilibrium stability we were told that second derivate of potential can be used. How?

I've made a quick google search, but couldn't find anything remarkable.

 

[Euclid]

If $$\frac{\partial^2U}{\partial x^2}$$ is positive then U is at a minimum (basic calculus - second derivative test). If instead it is negative then U is at a maximum. A point of equilibrium is stable if U is minimum and unstable if U is maximum.

 

[gulsen]

A point of equilibrium is stable if U is minimum and unstable if U is maximum.

I guess this because objects in a potential field tend move through where their potentials get lower?

 

[Physics Monkey]

Absolutely! After all, which way does the force point?