Plane rotations and Hamilton-Dirac mechanics

TL;DR

This paper develops a canonical formalism for SO(2), illustrating its role as a toy model for Hamilton-Dirac mechanics with constraints, and explicitly constructs the Lagrangian and Hamiltonian with their physical interpretations.

Contribution

It introduces a canonical formalism for SO(2) as a simplified model of Hamilton-Dirac mechanics, including explicit constructions and analysis of constraints.

Findings

Lagrangian and Hamiltonian formulations are explicitly constructed.

The canonical equations coincide with Lie equations.

Constraints satisfy CCR and are consistent.

Abstract

Canonical formalism for SO(2) is developed. This group can be seen as a toy model of the Hamilton-Dirac mechanics with constraints. The Lagrangian and Hamiltonian are explicitly constructed and their physical interpretation are given. The Euler-Lagrange and Hamiltonian canonical equations coincide with the Lie equations. It is shown that the constraints satisfy CCR. Consistency of the constraints is checked.