Finsler connection for general Lagrangian systems
Abstract
We give a Finsler non-linear connection by a new simplified definition for not only regular case but also singular case. In regular case, it corresponds to non-linear connection part of Berwald's connection, but our connection is expressed not in line element space but in point-Finsler space. In this view we recognize Finsler metric L(x,dx) as a non-linear form, which is a natural generalisation of Riemannian metric having original expression, \sqrt{g_{ab}(x)dx^a dx^b}. Furthermore our formulae provide easier calculation rather than conventional treatments, so we think that they suits to application to physics. Our definition can be used in the singular case of Finsler metric, which correspond to gauged constraint systems in mechanics. Here we give some non trivial examples of constraint systems for exposition of validity of our connection.
Keywords
Cite
@article{arxiv.1408.2322,
title = {Finsler connection for general Lagrangian systems},
author = {Laszlo Kozma and Takayoshi Ootsuka},
journal= {arXiv preprint arXiv:1408.2322},
year = {2016}
}
Comments
19pages. We have modified our definition of Finsler connection on the first version. This modification makes that more natural generalization of the usual non-linear connection which can be defined only on regular Finsler manifolds