How Does Charge and Elasticity Affect Hamiltonian Dynamics?

[pepediaz]

Homework Statement

Not homework exactly :-[

Relevant Equations

H = T + U (I posted an attempt to the solution below)

Let a mass m charged with q, attached to a spring with constant factor k = mω ^2 in an electric field E(t) = E0(t/τ) x since t=0.
(Equilibrium position is x0 and the deformation obeys ξ = x - x0)

What would the hamiltonian and motion equations be in t ≥ 0, in terms of m and ω?? Despise magnetic field.

 

[PeterDonis]

Moderator's note: Moved to homework forum.

 

[PeterDonis]

@pepediaz please provide relevant equations and your attempt at a solution.

 

[pepediaz]

2) It is correct to assume time symmetry and so equate this "energy function" to the canonic hamiltonian?
3) Motion equations come from hamiltonian or from lagrangian?

Thanks

 

[PeterDonis]

Here's my hamiltonian.

We cannot accept equations in images. Please use the PF LaTeX feature to post equations. You can find help on it here:

https://www.physicsforums.com/help/latexhelp/

 

[pepediaz]

But it is okay to have the development in the picture??

 

[PeterDonis]

But it is okay to have the development in the picture??

No. As I said, you need to use the PF LaTeX feature for equations. I gave you the link to the help page for it.

 

[pepediaz]

Is it okay to do it in RuBbEr??

Period

 

[PeterDonis]

Is it okay to do it in RuBbEr??

I have no idea what that is, but I assume it's not LaTeX. LaTeX is the only option you have here for posting equations. If you cannot or will not use LaTeX, we cannot help you.