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Equilibrium stability

  1. Apr 9, 2006 #1
    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.
  2. jcsd
  3. Apr 9, 2006 #2
    If [tex]\frac{\partial^2U}{\partial x^2}[/tex] is postive 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.
  4. Apr 9, 2006 #3
    I guess this because objects in a potential field tend move through where their potentials get lower?
  5. Apr 9, 2006 #4

    Physics Monkey

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