A variational method of deriving the equations of the non-linear mechanics of liquid crystals

The non-linear equations of the dynamics of liquid crystals [1], derived previously by the Poisson brackets method, are derived from the Hamilton-Ostrogradskii variational principle. The variational problem of an unconditional extremum of the action functional in Lagrange variables is investigated. The difference between the volume densities of the kinetic and free energy of the liquid crystal is used as the Lagrangian. It is shown that the variational equations obtained are equivalent to the differential laws of conservation of momentum and the kinetic moment of the liquid crystal in Euler variables, while the Ericksen stress tensor and the molecular field are defined in terms of the derivatives of the free energy. (C) 1999 Elsevier Science Ltd. All rights reserved.