Lagrangian and Euler-Lagrange equation question

[Sekonda]

Hey,

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 :

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

and for the 'r' EL equation I get:

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

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,
Thanks,
SK

 

[CompuChip]

From $\frac{d}{dt} m_1 r^2 \dot\theta = 0$ you can conclude that $m_1 r^2 \dot\theta = k$.

 

[Sekonda]

Thanks

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...

Cheers!
SK