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Parallel LCs circuit Lagrangian

  1. Nov 12, 2011 #1
    1. The problem statement, all variables and given/known data
    Hi, i have a quick question to see if i'm on the right track (I totally suck at electrical circuits since i never took a formal course so it might seem elementary to you.. anyway):

    Three LC systems in parallel with different L and C values, nothing else. closed circuit.
    First step in the problem is to formulate the Lagrangian and that's where i need a check, i'll be fine with the rest.

    3. The attempt at a solution
    Is it correct to write for the system:
    L =T+V=[itex]\frac{1}{2}[/itex][itex]\sum L_{i}\dot{q}^{2}_{i}+q^{2}_{i}/C_{i}[/itex]
    With the constraint:
    q[itex]_{1}[/itex]+q[itex]_{2}[/itex]+q[itex]_{3}[/itex]=0
    ??
    It seems too simple to me and i think i should be dealing with cross-terms, so a hint would be greatly appreciated.. thanks!
     
  2. jcsd
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