Affine n-dimensional Statics, affine screws and Grassmann algebra

The theory of screws is generalized to yield a formulation of Statics in higher-dimensional spaces in the absence of any distinguished metric structure. This level of generality necessitates the use of the tools of the exterior algebra of multi-vectors. The minimal structure retained serves to bring into relief the essential difference between screws and counter-screws as well as a weak version of the notion of rigid-body velocity field. An essential feature of the theory is the introduction of higher-order forces and displacements, whose relevance in the context of structured media can be determined in specific potential applications.