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Hooke's law theory question

  1. Jun 14, 2010 #1
    I am working on a theory and this thing is bothering since the past few hours...

    When we write down hooke's law that is

    d{2}x/dt{2} = -kx

    We write down as x as the displacement from the mean position given that the mean position coincides with zero...

    Now lets suppose that i have a 3D system.. And a sphere attached with various spheres... Lets say that the sphere we are interested in is (i,j). And out of the several spheres attached to ij lets say we take (i,j-1).

    The question is what is my hookes law equation.. Is it

    1) d{2}r{ij}/dt{2} = -[some constant][r{i,j} - r{i,j-1}]


    2) d{2}r{ij}/dt{2} = -[some constant][r{i,j-1} - r{i,j}]

    Now it is not that easy.. Cause i need to generalize this.. I have several other spheres attached with (i,j).. And if i use 1 it causes problem with some of the spheres and is okay for the rest... And if i use 2 it causes the same problem...

    I cant use 1 for some spheres and 2 for others... Cause then in my 3D infinite space the equations will depend on the position of the spheres...And the eqautions would be a mess to solve and the most important it loses its beauty...
  2. jcsd
  3. Jun 15, 2010 #2
    When things get complicated the mathematical beauty and symmetry has a tendency to fade. In some cases though, new beauty and symmetry can emerge out of complexity. In this case I cant help but think of the classic 3 body problem. I think you can get some simple and describable modes out of such a system, but in general - yea, it gets messy.

    Im interested to see some real replies. :p
  4. Jun 15, 2010 #3
    The three body problem is elegant... But in that case there are no complexities involved cause there are just three equations and its easy solving them... So looking at the three body problem wouldnt help...
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