Deriving a Hamiltonian from dimensionless equations

[thrillhouse86]

Hey all,

(As I mentioned in my previous post) I am trying to derive the Hamiltonian for a aeroelastic system, where the dynamical equations of motion (determined by Newtonian Mechanics) are known.

My process has been to
1. "guess" a form of the Lagrangian, check that it recreates the equations of motion
2. determine the canonical momentum
3. Perform a Legendre transform from the Lagrangian to the Hamiltonian

I've been thinking recently though, that the equations of motion are in dimensionless form (i.e. the equations have been appropriately scaled so that they are unitless). My question is:
Is it acceptable to derive the Hamiltonian from the dimensionless equations of motion, or do I have to use the "undimensionalised" equations of motion ? -

My rationale for this question is that the Hamiltonian does have to give me the total energy of the system - and I'm not sure that working from dimensionless equations will give me that ...

Cheers,
Thrillhouse

 

[Almsco]

Hi Thrillhouse,

It sounds like you're on the right track and have done a lot of work already. I think it is better to use the "undimensionalised" equations of motion when deriving the Hamiltonian, as that will give you the total energy of the system. The dimensionless equations might not provide the correct results. Good luck with your research!