Publication date:
Available online 4 April 2017
Source:Differential Geometry and its Applications
Author(s): S.G. Elgendi, Z. Muzsnay
In this paper we are investigating variational homogeneous second order differential equations by considering the question 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.