Freedom of h(2)-variationality and metrizability of sprays
Classical Analysis and ODEs
2016-09-22 v1 Differential Geometry
Abstract
In this paper we are investigating variational homogeneous second order differential equations by considering the questions of how many different variational principles exist for a given spray. We focus our attention on h(2)-variationality; that is, the regular Lagrange function is homogeneous of degree two in the directional argument. Searching for geometric objects characterizing the degree of freedom of h(2)-variationality of a spray, we show that the holonomy distribution generated by the tangent direction to the parallel translations can be used to calculate it. As a working example, the class of isotropic sprays is considered.
Keywords
Cite
@article{arxiv.1609.06581,
title = {Freedom of h(2)-variationality and metrizability of sprays},
author = {Salah G. Elgendi and Zoltán Muzsnay},
journal= {arXiv preprint arXiv:1609.06581},
year = {2016}
}
Comments
11 pages