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arXiv · 1609.06581

Freedom of h(2)-variationality and metrizability of sprays

Salah G. Elgendi·Zoltán Muzsnay
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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.

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Salah G. Elgendi, Zoltán Muzsnay. 2016-09-15. Freedom of h(2)-variationality and metrizability of sprays. https://arxiv.org/abs/1609.06581

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