  It is well known that Lagrangian dynamical systems naturally arise in
describing wave front dynamics in the limit of short waves (which is called
pseudoclassical limit or limit of geometrical optics). Wave fronts are the
surfaces of constant phase, their points move along lines which are called
rays. In non-homogeneous anisotropic media rays are not straight lines. Their
shape is determined by modified Lagrange equations. An important observation is
that for most usual cases propagating wave fronts are perpendicular to rays in
the sense of some Riemannian metric. This happens when Lagrange function is
quadratic with respect to components of velocity vector. The goal of paper is
to study how this property transforms for the case of general (non-quadratic)
Lagrange function.
