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: Hamilton and Lagrange functions

  1. Dec 10, 2009 #1
    The hamilton function of a particle in two dimensions is given by

    H = (p[tex]\stackrel{2}{x}[/tex])/2m + (p[tex]\stackrel{2}{y}[/tex])/2m + apxpy + U(x,y)
    Obtain the Hamiltonian equations of motion. Find the corresponding Lagrange function and Lagrange equations.

    Would it be px = dH/dpy (of course it would be partial)
    and py = - dH/dpx ?
    and how do we take into account the potential?
     
  2. jcsd
  3. Dec 11, 2009 #2

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    No, Hamilton's equations of motion are [tex]\dot{p_i}=-\frac{\partial H}{\partial q_i}[/tex] qnd [tex]\dot{q_i}=\frac{\partial H}{\partial p_i}[/tex], where [itex]q_i[/itex] are the generalized coordinates and [itex]p_i[/itex] are there corresponding momenta.

    In this case, your generalized coordinates are [itex]x[/itex] and [itex]y[/itex] (i.e. [itex]q_1=x[/itex] and [itex]q_2=y[/itex]) )and there corresponding momenta are [itex]p_x[/itex] and [itex]p_y[/itex] (i.e. [itex]p_1=p_x[/itex] and [itex]p_2=p_y[/itex])....
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook