Analytic Mechanics of Locally Conservative Physical Systems

TL;DR

This paper develops a generalized Lagrangian and Hamiltonian framework to analyze the dynamics of constrained physical systems influenced by locally conservative forces represented by closed differential forms.

Contribution

It introduces a novel formalism extending classical mechanics to systems with forces described by closed but non-exact differential forms on submanifolds.

Findings

Generalized equations of motion for locally conservative systems

Framework accommodates non-exact differential force fields

Provides tools for analyzing constrained dynamics with local conservation laws

Abstract

The analysis of the dynamics of a material point perfectly constrained to a submanifold of the three-dimensional euclidean space and subjected to a locally conservative force's field, namely a force's field corresponding to a closed but not necessarily exact differential form on such a submanifold, requires a generalization of the Lagrangian and the Hamiltonian formalism that is here developed.