Lagrangian formalism and conservation laws for electrodynamics in nonlinear elastic dielectrics

✍ Scribed by H Schoeller; A Thellung

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 982 KB
• Volume: 220
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(92)90324-f

✦ Synopsis

For the continuum theory .of electromagnetic fields in interaction with an elastic dielectric medium a new Lagrangian formalism is developed. The medium may be arbitrarily nonlinear and anisotropic, but in order to have conservation of quasimomentum it has to be homogeneous. For simplicity, the frequencies of the excitations are assumed to be such that dispersion can be neglected, but it is indicated how it can be taken into account. Directly from the Lagrangian equations of motion and alternatively by means of Noether's theorem the general conservation laws for energy, momentum, and quasimomentum are derived. They are formulated in both local (Eulerian) and material (Lagrangian) coordinate systems. Special attention is given to quasimomentum. Its density in local coordinates xkr where x = y + u (y, = material coordinates, u(y, t) = displacement vector of the elastic medium), is given by The first two terms are the well-known expressions for the electromagnetic and the elastic quasimomentum. The third, mixed, term is new. It can only be found if the difference between local and material coordinates is taken fully into account.