Orientation mechanics of liquid crystals. Transition to a local coordinate system

Equations of orientation mechanics of liquid crystals, written in a local rotational coordinate system related to the director orientation, are considered. A condition is obtained, which ensures qualitative similarity between solutions predicted by an approximate (single-constant) model and solutions obtained with the original formulation of the problem. Equations that provide a more exact approximation to the general model are proposed. The use of matrices in recording of energy relations allows a fairly easy transition to other coordinate systems and studying more sophisticated models for the description of the orientation state of liquid crystals. A transition to a local coordinate system makes it possible to compute three-dimensional liquid-crystal structures on moderate-performance personal computers.