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Lagrangian hamiltonian mech COC Goldstein 8.27

  1. Feb 21, 2012 #1
    1. The problem statement, all variables and given/known data

    a) the lagrangian for a system of one degree of freedom can be written as.

    L= (m/2) (dq/dt)2sin2(wt) +q(dq/dt)sin(2wt) +(qw)2

    what is the hamiltonian? is it conserved?

    b) introduce a new coordinate defined by

    Q = qsin(wt)

    find the lagrangian and hamiltonian with the new coordinate and is it conserved?



    2. Relevant equations

    qp-L = H

    3. The attempt at a solution

    Just wondering what the method is to solve b) or is it as simple as

    q = Q/sin(wt)

    (dq/dt) = (dQ/dt)/sin(wt) - Qwcos(wt)/(sin2(wt))

    subbing that in and solving?

    I'm assuming that this change of coordinate is supposed to make the Hamiltonian independent of time and therefore conserved.

    Yet what i found is not conserved, so i assume i used the wrong method.
     
  2. jcsd
  3. Feb 23, 2012 #2

    fluidistic

    User Avatar
    Gold Member

    Looks like a reasonable and straightforward method that you've used. How did you check out that the Hamiltonian wasn't conserved? I'd derivate it with respect to time and see if that equals 0.
     
  4. Feb 24, 2012 #3
    Well isnt that always how you check if its conserved? Thanks for replying didnt think anyone would reply.
     
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