1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Equation of motion from Hamiltonian

  1. Aug 17, 2015 #1
    1. The problem statement, all variables and given/known data
    [tex]H=\sum^N_{i=1}(\frac{p_i^2}{2m}+\frac{1}{2}(x_{i+1}-x_i)^2+(1-\cos(2\pi x_i))[/tex]

    2. Relevant equations
    Hamilton equation of motion I suppose
    ##\dot{q}=\frac{\partial H}{\partial p}##
    ##\dot{p}=-\frac{\partial H}{\partial q}##



    3. The attempt at a solution
    If particles are identical then
    ##\dot{p}=m \dot{x}##
    So if I understand well I will get from here system of equations
    ##\dot{p_1}=-\frac{\partial H}{\partial x_1}##
    If I take for example m=1, then
    ##\dot{x_1}=-\frac{\partial H}{\partial x_1}##
    Is this correct?
     
  2. jcsd
  3. Aug 17, 2015 #2

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    2017 Award

    no. Check the dimensions.
     
  4. Aug 18, 2015 #3
    Ok. Can I get some help?
     
  5. Aug 18, 2015 #4

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    2017 Award

    Yes: write down the dimensions and check,
     
  6. Aug 18, 2015 #5
    In particular I think BvU is trying to draw your attention to the partial derivatives you wrote in your last statements. Check those dimensions to see if they are consistent with the definitions you wrote in the relevant equations section.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted