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Expressing start of a vector using a point on the vector

  1. Jul 8, 2010 #1
    Hi guys. I hope this is the right thread for my question. The question is for my project and I can assure you it's not my homework. I know the solution to my problem isn't that complicated but I just lost my self with the problem and I don't have any one to talk with about my problem.

    Anyhow, here is my problem. I need to find the forces between two rods. Each rod is constructed from 3 particles (O--O--O) and the potential between the rod is given by:
    [tex]U = f(\bar r) \cdot g(\bar u_1 - \bar u_2) [/tex].


    Where

    [tex] \bar r = \bar r_{22} - r_{21} [/tex]

    That is, [tex] r [/tex] is the distance between the two middle particles. [tex] \bar u_i [/tex] is give by

    [tex] \bar u_i = \bar r_{i3} - \bar r_{i1} [/tex]

    which means it is the vector that shows the direction of the rod. I need to find forces between the particles:

    [tex] F = \frac{dU}{dr} [/tex].

    My problem is with the derivative of [tex] \bar u_1 - \bar u_2 [/tex] with respect to [tex] \bar r [/tex]. I tried several ways but I alway end up with [tex] \frac{du_1}{d \bar r} - \frac{du_2}{d \bar r} [/tex].

    What have I missed?

    Thanks.
     
  2. jcsd
  3. Jul 8, 2010 #2

    HallsofIvy

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    Yes, that is what you should end up with. Now what is the real difficulty?
     
  4. Jul 11, 2010 #3
    The problem is to express the derivative as a function of the distance between the two vectors.
    Thanks
     
  5. Jul 11, 2010 #4
    Which you did. So what is the difficulty ?
     
  6. Jul 13, 2010 #5
    I don't know how to compute the derivative. I feel like I'm missing something here
     
  7. Aug 15, 2010 #6
    Hi, I'm bumping the problem up again.
    I'll try to clarify my problem. I need to find the forces on ball number 1 and ball number 3 of each chain. I know that it should have something with the distance between the balls ([tex]\vec{r}_1 - \vec{r}_2[/tex]) and the angle ([tex]\theta[\tex]) but I'm not sure what it is.

    Thanks.
     
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