Geometry of Mechanics
Mathematical Physics
2025-05-07 v2 High Energy Physics - Theory
Differential Geometry
math.MP
Abstract
The aim of this work is to study the geometry underlying mechanics and its application to describe autonomous and nonautonomous conservative dynamical systems of different types; as well as dissipative dynamical systems. We use different geometric descriptions to study the main properties and characteristics of these systems; such as their Lagrangian, Hamiltonian and unified formalisms, their symmetries, the variational principles, and others. The study is done mainly for the regular case, although some comments and explanations about singular systems are also included.
Cite
@article{arxiv.2401.12650,
title = {Geometry of Mechanics},
author = {Miguel C. Muñoz-Lecanda and Narciso Román-Roy},
journal= {arXiv preprint arXiv:2401.12650},
year = {2025}
}
Comments
234 pages. These notes are a preliminary and partial version of the contents of the homonymous book