On the relation between tensor and vector approaches of nematodynamics

In this paper the relationship between tensorial and vector approaches for elastodynamics is examined in the framework of continuum theory of nematics. It will be elucidated that the Lagrange multipliers are required in the tensorial framework as well as the vector framework to assure equivalence between them. A contraction for the tensorial indices in the the time- dependent Ginzburg-Landau equation will be found eventually to result in the vector form concerned with the Ericksen-Leslie equation without flow dynamics.