Symmetries and Reduction. Part II - Lagrangian and Hamilton-Jacobi picture

TL;DR

This paper extends the analysis of symmetries and reduction in classical dynamics by exploring Noether's theorem within the Lagrangian and Hamilton-Jacobi frameworks, building on prior work.

Contribution

It introduces a Noether theorem related to symmetries and reduction procedures specifically for the Lagrangian and Hamilton-Jacobi formalisms.

Findings

Establishes a connection between symmetries and conserved quantities in these formalisms.

Provides a systematic reduction procedure based on symmetries.

Builds on previous work to deepen understanding of classical dynamics.

Abstract

Following the analysis we have presented in a previous paper (that we refer to as [I]), we describe a Noether theorem related to symmetries, with the associated reduction procedures, for classical dynamics within the Lagrangian and the Hamilton-Jacobi formalism.