On two reinterpretations of Cosserat continuum: fiber bundle versus the motor calculus

Abstract

It is the purpose of this paper to reinterprete the original Cosserat continuum from the point of view of both the fiber bundles geometry and the non-Abelian motor calculus. The main ideas of Cosserats are best explained in terms of the moving reper which is synonymous with the procedure of gauging in physics as well as with the procedure of constructing a fiber bundle in pure geometry. On the other hand, the classical (linear) von Mises motor calculus is extended to a non-Abelian case. It also appears that this non-Abelian version of the von Mises concept is fully equivalent with the fiber bundle description.