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: Hamiltonian Mechanics

  1. Sep 16, 2010 #1
    1. A particle of mass m is in the environment of a force field with components: Fz=-Kz, Fy=Fx=0 for some constant K. Write down the Hamiltonian of the particle in Cartesian coordinates .What are the constant of motion?



    2. H=kinetic energy +potential energy



    3. Is the Hamiltonian H is just E= int(-K)dz = -Kz??
    Also, I would like to ask what is the meaning of the constant of motion?? I really don't know where to start .

    That is the first time that I deal with the Hamiltonian Mechanics. I don't sure how to do the problem.:cry:
     
  2. jcsd
  3. Sep 16, 2010 #2

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    No, that's not the Hamiltonian. The Hamiltonian, as you noted, can be written as the sum of the kinetic and potential energies. The kinetic energy is just 1/2 mv2, which you will want to express in terms of the components of the particle's momentum. For the potential energy, you want to find the function V(x,y,z) such that F = -∇V.

    A constant of motion is simply a conserved quantity. If you write down Hamilton's equations for your Hamiltonian, you'll find the time derivative of two variables is equal to 0. Those two variables are therefore constant.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook