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Equilibrium from multivariable potential energy

  1. Feb 5, 2014 #1
    1. The problem statement, all variables and given/known data
    Three masses are disposed in a circular lane and linked with springs (resting lengths Lo). Find the potential energy and, from it, the equilibrium positions. (see image: https://www.dropbox.com/s/evqcspwlj68p5n9/2014-02-05 16.07.07.jpg )


    2. Relevant equations



    3. The attempt at a solution

    I have no problems finding the potential energy, but I'm not sure how to find the equilibrium positions from it. Should I derive respect each coordinate separately and get three expresions that i have to equate with 0? Or do a triple partial derivative [itex]\frac{\partial V}{\partial \phi_1 \partial \phi_2 \partial \phi_3}[/itex]and the equal that to 0?
     
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  3. Feb 5, 2014 #2

    TSny

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    What can you say about the potential energy function at a point of equilibrium?
     
  4. Feb 5, 2014 #3
    That it is a stationary point. However in this case I have three variables, so I'm not sure if it is enough with equating the derivatives to 0 or if I need to use something more advanced like Lagrange multipliers.
     
  5. Feb 5, 2014 #4

    TSny

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    Stationary point is right. So equating each first derivative to 0 should do it.
     
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