  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.
