Affine structure on Weil bundles

For every r-th order Weil functor T^A, we introduce the underlying k-th order Weil functors T^Ak, k = 1, . . . , r - 1. We deduce that T^AM → T^{Ar - 1} M is an affine bundle for every manifold M. Generalizing the classical concept of contact element by C. Ehresmann, we define the bundle κT^A M of contact elements of type A on M and we describe some affine properties of this bundle.