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Simple pendulum equation of motion

  1. Oct 15, 2014 #1
    Hi! I've been trying to find the equation of motion for the simple pendulum using x as the generalized coordinate (instead of the angle), but I haven't been able to get the right solution...

    1. The problem statement, all variables and given/known data

    The data is as usual, mass m, lenght l and gravity g. The X,Y axes origin can be anywhere I choose.

    2. Relevant equations

    Equation of motion using Lagrange equiations.


    3. The attempt at a solution

    This is the solution I'm supposed to find:

    [x''+(x*x'^2)/sqrt(l^2-x^2)+(g*x*sqrt(l^2-x^2))/l^2]=0

    (Sorry if it's a bit messy, I don't know how to type equations)

    But I get other terms I can't get rid of and I don't know what I'm doing wrong... I'd appreciate any help! Thanks!

    Edit: The extra term I get is (x'^2*x'')/sqrt(l^2-x^2) and also (2*g*x')/(sqrt(l^2-x^2)) instead of (g*x*sqrt(l^2-x^2))/l^2.

    (Still don't know how to post equations)
     
    Last edited: Oct 15, 2014
  2. jcsd
  3. Oct 15, 2014 #2

    Orodruin

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    It would help if you actually showed us your attempt with the extra terms. Also, use of the homework template is mandatory, do not erease the template headings.
     
  4. Oct 15, 2014 #3
    Sorry about the template, already corrected that and also added my extra terms. I'm still trying to solve it (not just waiting for an answer here) so I'll update it if I get it right. Thank you!
     
  5. Oct 15, 2014 #4

    vela

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  6. Oct 15, 2014 #5
    Ok, this is what I've got so far (although you could've asked nicely), sorry it's in Spanish:

    la foto.jpg

    And the solution I need to get to:

    Péndulo.png

    Anyway, thank you for your help.
     
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