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Homework Help: Lagrangian and Euler-Lagrange equation question

  1. May 2, 2013 #1

    I'm having trouble with part (d) of the question displayed below:


    I reckon I'm doing the θ Euler-Lagrange equation wrong, I get :

    [tex]\frac{\mathrm{d} }{\mathrm{d} t}(\frac{\partial L}{\partial \dot{\theta}})-\frac{\partial L}{\partial \theta}=\frac{\mathrm{d} }{\mathrm{d} t}(m_{1}r^{2}\dot{\theta})=0[/tex]

    and for the 'r' EL equation I get:

    [tex]\frac{\mathrm{d} }{\mathrm{d} t}(\frac{\partial L}{\partial \dot{r}})-\frac{\partial L}{\partial r}=m_{1}\ddot{r}+m_{2}\ddot{r}-m_{1}r\dot{\theta}^{2}-m_{2}g=0[/tex]

    In the theta equation I was originally just differentiating the theta with repsects to time, but the r^2 term also has a time dependence, I tried doing this and didn't know where to go from there... I'll have another go.

    Any comments are appreciated,
  2. jcsd
  3. May 2, 2013 #2


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    From ##\frac{d}{dt} m_1 r^2 \dot\theta = 0## you can conclude that ##m_1 r^2 \dot\theta = k##.
  4. May 2, 2013 #3

    Thanks I'll go and try that and see where that leads me, I think I tried this before but was obviously doing something wrong as the force wasn't central in the end...

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