Lejeune Dirichlet theorem

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 oscilation 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.

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matematikuvol	Lejeune Dirichlet theorem Tweet 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

M Quack	Lejeune Dirichlet theorem 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.