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intervoxel
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Homework Statement
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.
Homework 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]
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?
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