- #1

DannyJ108

- 25

- 2

- Homework Statement
- Draw the phase space in new canonical coordinates and the phase space of a single varying mass pendulum

- Relevant Equations
- H=p^2/2m+(1/2)kx^2

Hello everybody, new here. Sorry in advance if I didn't follow a specific guideline to ask this.

Anyways, I've got as a homework assignment two cannonical transformations (q,p)-->(Q,P). I have to obtain the hamiltonian of a harmonic oscillator, and then the new coordinates and the hamiltonian as a function of them (which is done correctly, I think).

I have to obtain the phase space in (Q,P) of this oscillator, but I have no idea how to. My question is how do I proceed to do so?

Also, another exercise I have is to obtain the solution to the equations of motion for a single varying-mass pendulum assuming small oscillations (sinx = x). I've proceeded introducing the rocket equation into the eq. of motion I've got, but I don't know if this is the correct way to do so. I have to obtain the phase space of this pendulum too, but no idea how to.

I would appreciate any help I can get regarding this, it would be extremely helpful.

Thanks fellow physicists.

Anyways, I've got as a homework assignment two cannonical transformations (q,p)-->(Q,P). I have to obtain the hamiltonian of a harmonic oscillator, and then the new coordinates and the hamiltonian as a function of them (which is done correctly, I think).

I have to obtain the phase space in (Q,P) of this oscillator, but I have no idea how to. My question is how do I proceed to do so?

Also, another exercise I have is to obtain the solution to the equations of motion for a single varying-mass pendulum assuming small oscillations (sinx = x). I've proceeded introducing the rocket equation into the eq. of motion I've got, but I don't know if this is the correct way to do so. I have to obtain the phase space of this pendulum too, but no idea how to.

I would appreciate any help I can get regarding this, it would be extremely helpful.

Thanks fellow physicists.