G. Askar Altay
Bogazici Univ., Istanbul, Turkey
M. Cengiz Dokmeci
Istanbul Tech. Universit-Teknik Univ., P.K.9, Taksim, 80191 Istanbul, Turkey
A unified procedure based on a general principle of physics (e.g.,
Hamilton's principle) together with Legendre's (or Friedrichs's) transformation
is proposed to systematically derive certain variational principles for
discontinuous electromagnetic fields which are useful to treat electromagnetic
waves and vibrations in dielectrics. The integral and differential types of
variational principles generate Maxwell's equations and the associated natural
boundary and jump conditions as well as the initial conditions, as their
Euler--Lagrange equations, for a regular finite and bounded dielectric region
with or without a fixed, internal surface of discontinuity. Special cases of
the variational principles, including a reciprocal one, are recorded which have
those for time-harmonic motions and a dielectric region within a vacuum or a
perfect conductor, and they are shown to agree with and to recover some of
earlier variational principles [e.g., M. C. Dokmeci, IEEE Trans. UFFC UFFC-35,
775--787 (1988); UFFC-37, 369--385 (1990) and G. A. Askar,