Lejeune Dirichlet theorem


by matematikuvol
Tags: dirichlet, lejeune, theorem
matematikuvol
matematikuvol is offline
#1
Apr3-12, 04:25 AM
P: 192
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
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M Quack
M Quack is offline
#2
Apr3-12, 04:53 AM
P: 640
The Lagrangian points L4 and L5.

http://en.wikipedia.org/wiki/Lagrangian_point
matematikuvol
matematikuvol is offline
#3
Apr3-12, 05:37 AM
P: 192
Ok. But Lejeune Dirichlet theorem is for small oscilation. I don't see any oscilation in here?

M Quack
M Quack is offline
#4
Apr3-12, 06:11 AM
P: 640

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.


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