Advanced Mechanics. Mathematical Introduction
Mathematical Physics
2010-01-20 v2 math.MP
Abstract
Classical non-relativistic mechanics in a general setting of time-dependent transformations and reference frame changes is formulated in the terms of fibre bundles over the time-axis R. Connections on fibre bundles are the main ingredient in this formulation of mechanics which thus is covariant under reference frame transformations. The basic notions of a non-relativistic reference frame, a relative velocity, a free motion equation, a relative acceleration, an external force are formulated. Newtonian, Lagrangian, Hamiltonian mechanical systems and the relations between them are defined. Lagrangian and Hamiltonian conservation laws are considered.
Cite
@article{arxiv.0911.0411,
title = {Advanced Mechanics. Mathematical Introduction},
author = {G. Giachetta and L. Mangiarotti and G. Sardanashvily},
journal= {arXiv preprint arXiv:0911.0411},
year = {2010}
}
Comments
107 pages