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Explain the proof in goldstein

  1. Jul 4, 2008 #1
    Question:
    Analyze the motion of a small bead attached to a wire which is rotating along a fixed axis?

    Proof(Using Lagrangian formulation):
    Clearly here the generalized coordinate is the distance of the particle along the wire.
    so we have the formulae
    [tex]\frac{d \frac{\delta T}{\delta r}}{dt} - \frac{\delta T}{\delta r}=Q[/tex]
    where [tex]Q[/tex] is the generalized force acting on the object ...
    goldstein claims that is 0 here i don't get that how?
     
  2. jcsd
  3. Jul 9, 2008 #2

    marcusl

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    First, correcting the typos, Lagrange's equation is

    [tex]\frac{d}{dt} \frac{\partial L}{\partial \dot{r}} - \frac{\partial L}{\partial r}=Q[/tex]

    There is no potential so L=T in this example as you have stated. In the method described on p. 26, the generalized force Q is zero because the constraint of moving along the wire is built into the generalized coordinates instead, and there are no non-conservative forces (i.e., friction).
     
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