  We introduce a complete gauge fixing for cylindrical spacetimes in vacuo
that, in principle, do not contain the axis of symmetry. By cylindrically
symmetric we understand spacetimes that possess two commuting spacelike Killing
vectors, one of them rotational and the other one translational. The result of
our gauge fixing is a constraint-free model whose phase space has four
field-like degrees of freedom and that depends on three constant parameters.
Two of these constants determine the global angular momentum and the linear
momentum in the axis direction, while the third parameter is related with the
behavior of the metric around the axis. We derive the explicit expression of
the metric in terms of the physical degrees of freedom, calculate the reduced
equations of motion and obtain the Hamiltonian that generates the reduced
dynamics. We also find upper and lower bounds for this reduced Hamiltonian that
provides the energy per unit length contained in the system. In addition, we
show that the reduced formalism constructed is well defined and consistent at
least when the linear momentum in the axis direction vanishes. Furthermore, in
that case we prove that there exists an infinite number of solutions in which
all physical fields are constant both in the surroundings of the axis and at
sufficiently large distances from it. If the global angular momentum is
different from zero, the isometry group of these solutions is generally not
orthogonally transitive. Such solutions generalize the metric of a spinning
cosmic string in the region where no closed timelike curves are present.
