Deriving a Hamiltonian from dimensionless equations

1. Sep 10, 2009

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