  This work presents the variational principles and the intrinsic versions of
several equations in field theories, in particular, for the Classical
Euler-Lagrange field equations, the implicit Euler-Lagrange field equations and
the non-holonomic implicit Euler-Lagrange field equations. The advantages of
the variational and intrinsic versions of these equations is that the
Lagrangians functions are not necessary regular Lagrangians. We present two
examples of this situation: Navier's equations and the non-holonomic Cosserat
rod. Finally we comment the Hamiltonian case when the Lagrangian is a
hyperregular function.
