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Classical Mechanics (Lagrangian)

  1. Oct 11, 2005 #1
    Hi,

    I'm looking for some advice on whether or not I'm doing a problem correctly.

    The problem is:
    A particle of mass m rests on a smooth plane. (the particle starts at r) The plane is raised to an inclination [tex]\theta[/tex], at a constant rate [tex]\alpha[/tex], with [tex]\theta = 0[/tex] at t=0, causing the particle to move down the plane.

    So, I'm taking the x to be the distance the particle travels down the slope.

    I come up with the following as the Lagrangian:

    [tex]L = \frac{1}{2} m\dot{x}^2 - mg(r-x)sin\theta[/tex]

    I'm not sure if this is correct.

    I would then get the equations of motion to be [tex]mgsin\theta - m\ddot{x}=0[/tex] and [tex]-mgsin(r-x)cos\theta=0[/tex].
     
    Last edited: Oct 11, 2005
  2. jcsd
  3. Oct 17, 2005 #2

    Tom Mattson

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    Sorry for the late reply. In case you're still interested, here's my response to this question.

    The KE term isn't right. It should have 2 terms, and one should contain an [itex]\alpha[/itex]. The PE term is OK.
     
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