CONSTRAINED BALLISTICS AND GEOMETRICAL OPTICS
The problem of constant-speed ballistics is studied under the um- brella of non-linear non-holonomic constrained systems. The Newtonian ap- proach is shown to be equivalent to the use of Chetaev's rule to incorporate the constraint within the initially unconstrained formulation. Although the re- sulting 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.