|Jan19-12, 01:49 PM||#1|
Hamiltonian mechanics electromagnetic field
1. The problem statement, all variables and given/known data
Let (V(x,t) , A(x,t)) be a 4-vector potential that constructs the electromagnetic field (in gaussian Units) by
E(x,t) = -∇V(x,t) - (1/c)δtA(x,t) , B = ∇xA , (x,t) elements of R3xRt
Consider the lagrangian
L=.5mv2 - eV(x,t) + (ev/c)(dot)A(x,t)
a) compute and interpret the Euler-lagrange equatinons of motion for this system
b) determine the hamiltonian
c) determine hamilton's equations of motion. Are they gauge invariant?
2. Relevant equations
3. The attempt at a solution
3 simple questions about this, and hopefully not too stupid of questions
when i apply the euler-lagrange equations do i take the curl of A or the gradient? if gradient what does that mean to take the ∇A?
is there only one equation of motion because i fail to see the other possibility if there is one.
Otherwise i can solve the rest
|euler, hamiltonian, lagrange|
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