Reformulation of the Dynamic Equations

In this Section we derive a particularly convenient and useful reformulation of the dynamic equations for nematic liquid crystals. The Ericksen-LesUe equations summarised in Section 4.2.5 can be reformulated in a manner similar to the reformulation of the equilibrium equations in Section 2.7 when it is supposed that 

Equations (2.211) to (2.216) remain valid for wp = WF 0a,Oa,i), but to make progress in the d3oiamic equations some further properties of the dissipation function must be investigated. It will be assumed throughout this Section that the inertial term involving crh is absent since, as mentioned above, it is considered to be negligible in most applications. 

As pointed out by Ericksen [80], when the Parodi relation (4.96) applies the vector gi and the viscous stress Uj in equations (4.77) and (4.86) can be obtained directly from the dissipation function V (which we can accept for our purposes as being defined by equation (4.97)), through the properties 

These properties can be verified directly by simple calculations. For example, since Ni = hi- NijTij by (4.9), 

We introduce reformulated versions of the potential in (4.112)3 and dissipation function V in (4.97) by 

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