Symmetries of line bundles and Noether theorem for time-dependent nonholonomic systems

TL;DR

This paper develops a framework for analyzing Noether symmetries in time-dependent nonholonomic systems with constraints and nonconservative forces, simplifying the derivation of momentum equations and conservation laws.

Contribution

It introduces a novel approach using characteristic line bundles to formulate Noether's theorem for complex time-dependent constrained systems.

Findings

Framework applies to systems with constraints and nonconservative forces

Simplifies the formulation of momentum equations

Provides a transparent derivation of Noether's theorem

Abstract

We consider Noether symmetries of the equations defined by the sections of characteristic line bundles of nondegenerate 1-forms and of the associated perturbed systems. It appears that this framework can be used for time-dependent systems with constraints and nonconservative forces, allowing a quite simple and transparent formulation of the momentum equation and the Noether theorem in their general forms.