Clebsch parameterization from the symplectic point of view

TL;DR

This paper introduces a symplectic framework to systematically derive canonical Lagrangian formulations for rotational systems by enlarging phase space with extra variables, overcoming previous obstructions.

Contribution

It presents a novel method to compute canonical Lagrangian formulations for rotational systems using symplectic geometry and phase space extension.

Findings

Obstruction to canonical formalism can be systematically overcome.

Multiple dynamically equivalent Lagrangian descriptions can be constructed.

Formalism applies generally to rotational systems.

Abstract

This work propose an alternative and systematic way to obtain a canonical Lagrangian formulation for rotational systems. This will be done in the symplectic framework and with the introduction of extra variables which enlarge the phase space. In fact, this formalism provides a remarkable and new result to compute the canonical Lagrangian formulation for rotational systems, {\it i.e.}, the obstruction to the construction of a canonical formalism can be solved in an arbitrary way and, consequently, a set of dynamically equivalent Lagrangian descriptions can be computed.