Noether's Theorem on Time Scales

TL;DR

This paper extends Noether's theorem to the calculus of variations on time scales, establishing a link between symmetries and conserved quantities in this unified framework.

Contribution

It introduces a Noether's theorem applicable to calculus of variations on time scales, unifying continuous and discrete cases.

Findings

Existence of conserved quantities for variational symmetries on time scales

Generalization of Noether's theorem to a broader mathematical setting

Application potential in dynamic systems analysis

Abstract

We show that for any variational symmetry of the problem of the calculus of variations on time scales there exists a conserved quantity along the respective Euler-Lagrange extremals.