Degenerated mechanics in a homogeneous continuum: potentials for spin and twist

In this paper we extend our considerations on the spin and twist motions in a homogenous continuum. Refering to our former results, we define the degenerated mechanics as that in which the displacement motions vanish while rotation motions, as the independent elastic fields, do exist. This is exactly the opposite case to the classic ideal elastic continuum in which only displacement motions are taken into account, while any independent rotation motions are excluded because of a lack of the appriopriate constitutive laws supporting the existence of an elastic response due to the rotational deformations of bonds in a lattice network. We propose a system of potentials which would help us to understand the waves and geometrical features of degenerated mechanics and its Riemannian geometry.