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Homework Help: Lagrangian dynamics problem.

  1. Oct 28, 2012 #1
    A point of mass m, affected by gravity, is obliged to be in a vertical plan on a parabola with equation z = a.r^2

    a is a constant and r is the distance between the point of mass m and the OZ vertical axis. Write the Lagrange equations in the cases that the plan of the parabola is :

    a) is fixed

    b) it rotates with angular speed ω about the OZ axis.


    I just need to know the equations of the position and speed.

    in a) i considered:

    x = r cosθ ||||| x' = r'cosθ - rθ'sinθ
    y = r sinθ ||||| y' = r'sinθ + rθ'cosθ
    z = a.r^2 ||||| z' = a.r^2'

    in b)

    x = r cos(wt) ||||| x' = r'cos(wt) - rwsin(wt)
    y = r sin(wt) ||||| y' = r'sin(wt)+ rwcos(wt)
    z = a.r^2 |||||| z' = a.r^2'

    Is that right?
  2. jcsd
  3. Oct 28, 2012 #2


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    For part (a) θ is fixed, hence θ' = ? I would think that without loss of generality you could let θ be zero.

    Part (b) looks good to me.
  4. Oct 28, 2012 #3

    considering that θ = 0, then part a) is not going to have the y component :)

    And other question:

    z' = a.r^2' or z' = 2.a.r'.r ? is that the same?
  5. Oct 28, 2012 #4


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  6. Oct 28, 2012 #5
    Thanks for all your the help!
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