Geometric Properties of Paths in Relativistic Lagrangian Mechanics
Mathematical Physics
2017-07-26 v1 General Relativity and Quantum Cosmology
math.MP
Abstract
Considering an extension of the principle of covarience to the action along a path in relativistic Lagrangian mechanics, we motivate the use of geometric -- i.e. covariant and parameter invariant -- Lagrangian functions. We then study some properties of geometric Lagrangians, and introduce the notion of deviation of a path, which is a covariant measure of how much a path departs from a geodesic. Finally, we apply this notion of the twin paradox, and provide a rigorous resolution of it.
Keywords
Cite
@article{arxiv.1707.07942,
title = {Geometric Properties of Paths in Relativistic Lagrangian Mechanics},
author = {Olivier Brunet},
journal= {arXiv preprint arXiv:1707.07942},
year = {2017}
}