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Lagrangian equations of motion

  1. Oct 12, 2011 #1
    1. The problem statement, all variables and given/known data

    Find equations of motion (eom) of a particle moving in a D-dimensional flat space with the following Lagrangian

    L = (1/2)mv2i - k/ra,

    r = root(x2i), m,k,a are constants


    2. Relevant equations



    3. The attempt at a solution

    The equations of motion are given by d/dt(∂L/∂vi) - ∂L/∂xi = 0

    So, when I work all this out I get
    ma = ka/xia+1

    I have a feeling this isn;t correct though.

    Am I doing the partials wrong?
     
  2. jcsd
  3. Oct 12, 2011 #2

    vela

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    Yes, you're taking the partial with respect to xi incorrectly. Try writing out the potential term in terms of the xi's and differentiating.

    Also why is a multiplying m? How did the exponent of r get over there?
     
  4. Oct 12, 2011 #3
    U = k/ra = k/root(x2i)a
    = k/xai
    = kx-ai

    Differentiating this with respect to xi gives -akx-a-1


    As for the last part; sorry, when I wrote a on the LHS I was referring to the second derivative of xi w.r.t. time
     
  5. Oct 12, 2011 #4

    vela

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    How are you going from k/root(x2i)a to k/xai?

    Are you saying, for instance, that [itex]\sqrt{x_1^2+x_2^2} = x_1+x_2[/itex]?

    EDIT: Oh, I see why we're getting different answers. I think there's an implied summation: [tex]r=\sqrt{x_i^2} = \sqrt{x_i x_i} = \sqrt{\sum_i x_i^2}[/tex]
     
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