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Lagrangian of dipole set

  1. Jan 18, 2014 #1
    1. The problem statement, all variables and given/known data

    Build the lagrangian of a set of N electric dipoles of mass m, length l and charge q.
    Find the equations of motion.
    Find the corresponding difference equations.

    2. Relevant equations
    Lagrange function
    [itex]L=T-V[/itex]

    Lagrange's equations
    [itex]\frac{d}{dt}\left(\frac{\partial L}{\partial \dot{x_k}}\right)-\frac{\partial L}{\partial x_k}=0[/itex]



    3. The attempt at a solution
    Electrostatic potential
    [itex]V=\sum\limits^{N/2}_{i=1} \frac{kq}{r_i}-\sum\limits^N_{i=N/2+1} \frac{kq}{r_i}[/itex]

    Kinetic energy
    [itex]T=\sum\limits^{N}_{i=1} \frac{1}{2}m\,v_i^2[/itex]

    Constraints
    [itex](r_j - r_i)-l^2=0[/itex]

    The system has N/2 degrees of freedom. (???)

    how the constraint condition defines the generalized coordinates?
     
    Last edited: Jan 19, 2014
  2. jcsd
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