For geometric systems of real principal type, we define a subprincipal symbol and
derive a transport equation for polarizations which, in the scalar case, is a well-known
equation of Duistermaat and Hörmander. We apply the transport equation to
propagation of polarization in transmission problems of elastodynamics, to interior
bulk waves as well as to free (Rayleigh) surface waves. Using spectral factorizations of
matrix polynomials having real spectrum, we establish reflection and refraction laws
of polarizations at the boundary and at interior interfaces. The results are not limited
to isotropic elasticity.
Keywords
subprincipal symbol, real principal type, linear
elastodynamics
