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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


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    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.
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