# An intrinsic definition of hamiltonian system

1. Jan 12, 2010

(Sorry for my poor English, Please, forgive mistakes, if any.)

Dear Friends

A system of second order, in normal form, differential equations can be rewritten as a similar first order one, in infinite way (usually that's done introducing simply auxiliaries variables, but it can also be accomplished by means of auxiliaries functions).

Now, each analytical mechanics exposure gives a "recipes" (the Legendre transform) to turn a lagrangian system into the associated hamiltonian; rather, I would know if a property exists such that, among the infinite first order systems equivalent to the given lagrangian one, only the associated hamiltonian enjoys it.

This could allow to express an intrinsic definition of the associated hamiltonian system, instead of merely declaring the way to get it.

Warmest regards.

Barabara Da Vinci
(Italy)