### Totally singular Lagrangians and affine Hamiltonians.

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The higher order bundles defined by an anchored bundle are constructed as a natural extension of the higher tangent spaces of a manifold. We prove that a hyperregular lagrangian (hyperregular affine hamiltonian) is a linearizable sub-lagrangian (affine sub-hamiltonian) on a suitable Legendre triple.

The aim of this paper is to study the projectable and $N$-projectable objects (tensors, derivations and linear connections) on the total space $E$ of a fibred manifold $\xi $, where $N$ is a normalization of $\xi $.

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