  The emergence of gauge particles (e.g., photons and gravitons) as Goldstone
bosons arising from spontaneous symmetry breaking is an interesting hypothesis
which would provide a dynamical setting for the gauge principle. We investigate
this proposal in the framework of a general $% SO(N)$ non-abelian Nambu model
(NANM), effectively providing spontaneous Lorentz symmetry breaking in terms of
the corresponding Goldstone bosons. Using a non-perturbative Hamiltonian
analysis, we prove that the $SO(N)$ Yang--Mills theory is equivalent to the
corresponding NANM, after current conservation together with the Gauss laws are
imposed as initial conditions for the latter. This equivalence is independent
of any gauge fixing in the YM theory. A substantial conceptual and practical
improvement in the analysis arises by choosing a particular parametrization
that solves the non-linear constraint defining the NANM. This choice allows us
to show that the relation between the NANM canonical variables and the
corresponding ones of the YM theory, $A_{i}^{a}$ and $E^{bj}$, is given by a
canonical transformation. In terms of the latter variables, the NANM
Hamiltonian has the same form as the YM Hamiltonian, except that the Gauss laws
do not arise as first class constraints. The dynamics of the NANM further
guarantees that it is sufficient to impose them only as initial conditions, in
order to recover the full equivalence. It is interesting to observe that this
particular parametrization exhibits the NANM as a regular theory, thus
providing a substantial simplification in the calculations.
