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: Conservation of Angular Momentum Using the Hamiltonian

  1. Oct 15, 2009 #1
    1. The problem statement, all variables and given/known data
    The Hamiltonian for a particle mass m, moving in a central force field is given as: H = 1/(2m) * |p^2| - V(r). Take the Hamiltonian to be invariant, such that it can be shown that L = r x p the angular momentum vector is a conserved quantity: dL/dt = {L,H} = 0.

    2. Relevant equations
    q_i-dot = dH/dp_i and p_i-dot = - dH/dq_i

    3. The attempt at a solution
    I do not understand how to go about solving the following problem ( I think I understand what the Hamiltonian is, but I do not understand how to from it to what needs to be proven) To solve the problem I believe I need to get from Hamiltonian's equations to Lagrange's p_i = dL/dx_i-dot and then from there use p-dot * dr + p * dr-dot = 0 where dr is defined as the distance between two vectors r and r+dr.
  2. jcsd
  3. Oct 15, 2009 #2


    User Avatar
    Homework Helper
    Gold Member

    Hi physics2018, welcome to PF!:smile:

    Well, since you are asked to show that [itex]\frac{d\textbf{L}}{dt}=\{\textbf{L},H\}=0[/itex], why not start by computing [itex]\{\textbf{L},H\}[/itex]?
    Last edited: Oct 15, 2009
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook