  The paper considers the general case of incompressible non-classical
elasticity with small deformations and rotations. The thermodynamic stability
is analysed for free energy density with three rotational degrees of freedom.
Although the theory generally predicts the stress to be non-symmetric, the
stress tensor can still be considered as symmetrical in the absence of external
fields and when the inertia effects of internal rotations and couple stresses
are neglected. When the condition of stress tensor symmetry is applied, it
results in simplified, "reduced" expressions for the free energy density and
stress, which preserve the general stability conditions and allow easy
calculations of stress-strain relations and rotations. Using this reduced
formulation, a general condition of existence of soft deformations is analysed
for the weak nematic elasticity. The reduction procedure is exemplified using
the infinitesimal Warner potential derived from a molecular model.
