HAMILTONIAN APPROACH TO CONTINUUM DYNAMICS

A study is made of the problem of obtaining the Poisson-bracket algebr a of the dynamical variables of continuous media on the basis of speci fication of the kinematic part of the Lagrangian in terms of generaliz ed coordinates and momenta. Within this algebra, subalgebras of variab les corresponding to the description of elastic media, the hydrodynami cs of ordinary liquids, and the dynamics of some phases of liquid crys tals are identified. The differential conservation laws associated wit h the symmetries of the Hamiltonian of the system are studied. The dyn amics of nematics is considered, and features of the dynamics of the c holesteric, smectic, and discotic phases are noted.