Skip to main content

Abstract

For given time-independent Newtonian system of equations of motion and given Poisson Brackets allowed by these equations, it is proven that locally a Lagrangian exists that gives these equations of motion as its regular Euler-Lagrange equations, and gives these Poisson Brackets in a regular process of obtaining the Hamiltonian and its Poisson Brackets. However, this Lagrangian may be using generalized position-velocity variables instead of the original position-velocity variables from the original equations of motion. Also, Darboux Box variables are introduced to prove that all Newtonian dynamical systems are locally isomorphic, meaning that locally there exists a one-to-one function relating the variables describing both systems that preserves equations of motion, Poisson Brackets, the Hamiltonian and, in a sense, also the Lagrangian.

Files

File nameDate UploadedVisibilityFile size
Darboux_Box_Variables__Complete_sets_of_Lagrangians__Isomorphism_of_all_Systems__2018_02_17.pdf
19 Jul 2022
Public
292 kB

Metrics

Metadata