An algebraic approach to systems with dynamical constraints

TL;DR

This paper introduces an algebraic framework for systems with dynamical constraints, generalizing Noether's theorem to include constraints in phase space and relating constants of motion with local projectors.

Contribution

It presents a novel algebraic approach that extends Noether's theorem to systems with acceleration constraints in phase space.

Findings

Derived equations relate constants of motion to local projectors.

Generalized Noether's theorem for constrained systems.

Constraints incorporated directly into phase space analysis.

Abstract

Constraints imposed directly on accelerations of the system leading to the relation of constants of motion with appropriate local projectors occurring in the derived equations are considered. In this way a generalization of the Noether's theorem is obtained and constraints are also considered in the phase space.