Orientation analysis, tensor analysis and the group properties of the SI supplementary units. II (Q1084717)

An extension of the methods of dimensional analysis to include the orientations of physical quantities shows that a useful approach is to assign orientations to the supplementary units, radian and steradian, and to require that physical equations be orientationally as well as dimensionally homogeneous. Orientational symbols representing the intuitive orientational character are shown to form a noncyclic Abelian group with four members. The methods of dimensional analysis derive from the fact that the laws of physics must be independent of the units; orientational analysis derives from the fact that they must also be independent of the coordinate system, i.e. they are expressible as tensor equations.