Chapter 7 - Translational and Rotational Motion of a Uniaxial Liquid Crystal as Derived Using Hamilton's Principle of Least Action

Abstract

This chapter illustrates how rotational motion contributes to the conservative Hamiltonian dynamics of complex, anisotropic fluids, such as liquid crystals. This illustration is based on one of the most revered principles of classical mechanics, Hamilton's Principle of Least Action. The derivation presented in the chapter, follows logical and completely rigorous steps. Every component of the derivation has a sound basis in standard mathematics and well established physical principles. The new feature of the derivation follows the sound mathematics principles and applies them in a new way. In so doing, and why it must be accounted for when deriving models for materials g, it becomes obvious how rotational motion influences the dynamics of anisotropic fluid with such intricate microstructure. The conservative dynamics of the Leslie-Ericksen (LE) Model of a uniaxial liquid crystal that are rederived using Hamilton's Principle of Least Actions performs two purposes: firstly, they illustrates that variational principles are applied to very complicated fluidic materials and secondly, they derive the non-canonical Poisson bracket that generates the conservative dynamics of the LE Model.