Eikonal equation for moving media and its relation to dynamic programming

The eikonal equation for moving media (first order in V/c) is derived for the electromagnetic case. Maxwell's equations with Minkowski's constitutive relations, and the dynamic programming approach, lead to essentially the same result. The acoustical eikonal equation for moving media is derived by means of the dynamic programming method. A result obtained by Kritikos, believed to be wrong, is shown to be valid as an approximation.