  The problem of constant-speed ballistics is studied under the umbrella of
non-linear non-holonomic constrained systems. The Newtonian approach is shown
to be equivalent to the use of Chetaev's rule to incorporate the constraint
within the initially unconstrained formulation. Although the resulting
equations are not, in principle, obtained from a variational statement, it is
shown that the trajectories coincide with those of geometrical optics in a
medium with a suitably chosen refractive index, as prescribed by Fermat's
principle of least time. This fact gives rise to an intriguing mechano-optical
analogy. The trajectories are further studied and discussed.
