Is Stable Equilibrium Possible Without Potential Energy Minima?

[matematikuvol]

Lejeune Dirichlet theorem says that when potential energy has minima then equilibrium is stable, but that is sufficient condition. Can you give me example or examples where potential energy hasn't minima and equilibrium is stable. Tnx

 

[M Quack]

The Lagrangian points L4 and L5.

http://en.wikipedia.org/wiki/Lagrangian_point

 

[matematikuvol]

Ok. But Lejeune Dirichlet theorem is for small oscilation. I don't see any oscillation in here?

 

[M Quack]

These are stable points, but only in a dynamic, rotating system. Stable implies that you can have small oscillations around the point of equilibrium.

Actually, the rotation of planets around the sun would be a simpler example of a dynamic equilibrium.