Lagrangian of the system of two masses

[rouge89]

I am wondering, how does lagrangian of such system look like?

Will it be:

$$L=\frac{m_{1} \cdot \dot{y}^2}{2} + \frac{m_{2} \cdot \dot{x}^2}{2} +\frac{m_{3} \cdot (\dot{y'}^2+\dot{x'}^2)}{2} + \frac{I \cdot \dot{ \alpha }^2}{2} - mgy - mgy'$$

where:

$$y'=\frac{l}{2}sin(\alpha)$$
$$x'=\frac{l}{2}cos(\alpha)$$ ?

 

[andrien]

x^2+y^2=l^2,so x,y,ω(angular velocity)can be obtained.by the way that is correct

 

[Natey213]

I'm going to sit down and do this when I get a chance. But for now, it looks like you are only going to need one generalized coordinate to completely define the system. I would use the y-coord of m1.

 

[rouge89]

Hmm so guys, this is correct (with this additional equation as, andrien wrote: x^2+y^2=l^2), but there is way to do that better using one generalized coordinate, right? Hmm very often this one generalize is an angle + length... but here maybe it could be done with y,x etc.