Variational principle in the mechanics of liquid crystals

We present a variational derivation of equations of non-linear dynamics for a nematic liquid crystal that is regarded as a continuous medium consisting of anisotropic elongated molecules. The dynamic state of such an ''oriented'' medium is described by velocity, pressure and density fields, as well as by director field: The difference between volume densities of the kinetic and free energies of the liquid crystal is taken as a Lagrangian. A variational problem of absolute extremum of the functional of action is investigated in Lagrangian variables. The variational equations obtained are shown to be equivalent to local laws of conservation of mass and momentum of a liquid crystal in Euler variables. Copyright (C) 1996 Elsevier Science Ltd.