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Lagrangian of the system of two masses

  1. Jun 22, 2012 #1
    I am wondering, how does lagrangian of such system look like?


    Will it be:

    [tex]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' [/tex]


    [tex]y'=\frac{l}{2}sin(\alpha) [/tex]
    [tex]x'=\frac{l}{2}cos(\alpha) [/tex] ?
  2. jcsd
  3. Jun 23, 2012 #2
    x^2+y^2=l^2,so x,y,ω(angular velocity)can be obtained.by the way that is correct
  4. Jun 24, 2012 #3
    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.
  5. Jun 25, 2012 #4
    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.
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